Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

2074 East Hall

530 Church Street

Ann Arbor, MI 48109-1043

United States

  • University of Michigan at Ann Arbor - Department of Mathematics

SCHOLARLY PAPERS

80

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146

Scholarly Papers (80)

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1.

Large Tournament Games

Number of pages: 57 Posted: 12 Feb 2018 Last Revised: 05 Nov 2018
Erhan Bayraktar, Jaksa Cvitanic and Yuchong Zhang
University of Michigan at Ann Arbor - Department of Mathematics, California Institute of Technology - Division of the Humanities and Social Sciences and University of Toronto - Department of Statistics
Downloads 330 (152,695)
Citation 9

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Tournaments, rank-based rewards, mechanism design, mean field games, bifurcation diagram of Nash equilibria

2.

A Macroeconomic SIR Model for COVID-19

Number of pages: 23 Posted: 29 Jun 2020
Erhan Bayraktar, Asaf Cohen and April Nellis
University of Michigan at Ann Arbor - Department of Mathematics, University of Michigan at Ann arbor - Department of Mathematics and University of Michigan
Downloads 262 (194,142)
Citation 1

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Epidemic modeling, COVID-19, planner problem, value iterations, exit time control problem

3.

Mini-Flash Crashes, Model Risk, and Optimal Execution

Number of pages: 48 Posted: 30 May 2017
Erhan Bayraktar and Alexander Munk
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 258 (197,094)
Citation 4

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Flash Crash, Knightian Uncertainty, Model Error, Optimal Execution

4.

Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities

Journal of Economic Dynamics and Control, Vol. 33, No. 3, 2009
Number of pages: 25 Posted: 31 Jan 2009 Last Revised: 25 Jan 2014
Erhan Bayraktar, Moshe A. Milevsky, S. D. Promislow and V.R. Young
University of Michigan at Ann Arbor - Department of Mathematics, York University - Schulich School of Business, York University - Department of Mathematics & Statistics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 195 (256,894)
Citation 11

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Stochastic mortality, pricing, annuities, Sharpe ratio, non-linear partial differential equations, market price of risk, equivalent martingale measures

5.

High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering

Number of pages: 30 Posted: 14 May 2016
Erhan Bayraktar and Alexander Munk
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 182 (273,193)
Citation 2

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parimutuel wagering, large generalized games, nash equilibrium

6.

Optimal Investment to Minimize the Probability of Drawdown

Stochastics, Forthcoming
Number of pages: 15 Posted: 18 Feb 2016
Bahman Angoshtari, Erhan Bayraktar and V.R. Young
University of Miami - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 148 (325,590)

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Optimal investment, stochastic optimal control, probability of drawdown

7.

Quantile Hedging in a Semi-Static Market with Model Uncertainty

Number of pages: 28 Posted: 21 Aug 2014 Last Revised: 25 Sep 2017
Erhan Bayraktar and Gu Wang
University of Michigan at Ann Arbor - Department of Mathematics and Worcester Polytechnic Institute
Downloads 142 (336,487)

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Quantile hedging, Model Uncertainty, Semi-static Hedging, Neyman-Pearson Lemma

8.

Recombining Tree Approximations for Optimal Stopping for Diffusions

Number of pages: 27 Posted: 01 Mar 2017
Erhan Bayraktar, Yan Dolinsky and Jia Guo
University of Michigan at Ann Arbor - Department of Mathematics, ETH Zürich and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 127 (366,538)

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American Options, Optimal Stopping, Recombining Trees, Skorokhod Embedding

9.

Countercyclical Unemployment Benefits: General Equilibrium Analysis of Transition Dynamics

Number of pages: 35 Posted: 20 Sep 2021
Erhan Bayraktar, Indrajit Mitra and Jingjie Zhang
University of Michigan at Ann Arbor - Department of Mathematics, Federal Reserve Banks - Federal Reserve Bank of Atlanta and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 123 (375,426)

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10.

A Proof of the Smoothness of the Finite Time Horizon American Put Option for Jump Diffusions

SIAM Journal on Control and Optimization (2009), 48 (2), 551-572
Number of pages: 18 Posted: 23 May 2008 Last Revised: 25 Jan 2014
Erhan Bayraktar
University of Michigan at Ann Arbor - Department of Mathematics
Downloads 122 (377,736)
Citation 1

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Optimal Stopping, Markov Processes, Jump Diffusions, American Options, Integro-Differential Equations

11.

Time Consistent Stopping for the Mean-Standard Deviation Problem --- The Discrete Time Case

Number of pages: 27 Posted: 05 Mar 2018
Erhan Bayraktar, Jingjie Zhang and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 119 (384,681)
Citation 3

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Time-inconsistency, optimal stopping, liquidation strategy, mean-variance problem, subgame perfect Nash equilibrium

12.

Fundamental Theorem of Asset Pricing Under Transaction Costs and Model Uncertainty

Forthcoming, Mathematics of Operations Research
Number of pages: 24 Posted: 08 Feb 2014 Last Revised: 31 Aug 2015
Erhan Bayraktar and Yuchong Zhang
University of Michigan at Ann Arbor - Department of Mathematics and University of Toronto - Department of Statistics
Downloads 105 (420,825)
Citation 3

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Transaction costs, non-dominated collection of probability measures, Fundamental Theorem of Asset Pricing, martingale selection problem

13.

Arbitrage, Hedging and Utility Maximization Using Semi-Static Trading Strategies with American Options

Number of pages: 14 Posted: 26 Feb 2015 Last Revised: 27 Feb 2015
Erhan Bayraktar and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 92 (459,961)
Citation 2

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Fundamental theorem of asset pricing, hedging duality, utility maximization, semi-static trading strategies, American options

14.

On the Market Viability Under Proportional Transaction Costs

Number of pages: 34 Posted: 02 Feb 2014 Last Revised: 11 Apr 2016
Erhan Bayraktar and Xiang Yu
University of Michigan at Ann Arbor - Department of Mathematics and Hong Kong Polytechnic University
Downloads 91 (463,065)
Citation 4

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Proportional Transaction Costs, (Robust) No Unbounded Profit with Bounded Risk, Strictly Consistent Local Martingale Systems, (Robust) No Local Arbitrage with Bounded Portfolios, Utility Maximization, Market Viability, Numeraire Portfolios

15.

Outperforming the Market Portfolio with a Given Probability

The Annals of Applied Probability (2012), Vol. 22, No. 4, 1465-1494
Number of pages: 30 Posted: 01 Feb 2014
Erhan Bayraktar, Yu-Jui Huang and Qingshuo Song
University of Michigan at Ann Arbor - Department of Mathematics, University of Colorado at Boulder - Department of Applied Mathematics and City University of Hong Kong (CityU)
Downloads 89 (469,503)

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strict local martingale deflators, optimal arbitrage, quantile hedging, viscosity solutions, nonuniqueness of solutions of nonlinear PDEs

16.

Minimizing the Probability of Lifetime Ruin Under Ambiguity Aversion

SIAM Journal on Control and Optimization, 53(1), 58-90, 2015
Number of pages: 35 Posted: 07 Feb 2014 Last Revised: 09 May 2015
Erhan Bayraktar and Yuchong Zhang
University of Michigan at Ann Arbor - Department of Mathematics and University of Toronto - Department of Statistics
Downloads 87 (476,117)
Citation 2

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Probability of lifetime ruin, ambiguity aversion, drift uncertainty, viscosity solutions, Perron’s method, regularity

17.

On Hedging American Options Under Model Uncertainty

Number of pages: 20 Posted: 27 Jan 2014
Erhan Bayraktar, Yu-Jui Huang and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics, University of Colorado at Boulder - Department of Applied Mathematics and The University of Sydney
Downloads 86 (479,549)
Citation 3

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American options, model independent pricing, semi-static hedging strategies

18.

Convergence of Optimal Investment Problems in the Vanishing Fixed Cost Limit

Number of pages: 29 Posted: 02 Feb 2022
Erhan Bayraktar, Christoph Belak, Frank Thomas Seifried and Sören Christensen
University of Michigan at Ann Arbor - Department of Mathematics, Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften, University of Trier and Gothenburg University
Downloads 75 (519,667)

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Portfolio Optimization, Transaction Costs, Stochastic Perron's Method, Viscosity Solutions

19.

Super-Hedging American Options with Semi-Static Trading Strategies Under Model Uncertainty

Number of pages: 8 Posted: 28 May 2016
Erhan Bayraktar and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 68 (548,437)
Citation 2

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American options, super-hedging, model uncertainty, semi-static trading strategies, randomized models

20.

Stochastic Perron's Method for Hamilton-Jacobi-Bellman Equations

SIAM Journal on Control and Optimization, 51(6), 4274-4294, 2013
Number of pages: 21 Posted: 27 Jan 2014
Erhan Bayraktar and Mihai Sirbu
University of Michigan at Ann Arbor - Department of Mathematics and University of Texas at Austin
Downloads 68 (548,437)
Citation 2

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Perron's method, viscosity solutions, non-smooth verification, comparison principle

21.

A Note on the Fundamental Theorem of Asset Pricing Under Model Uncertainty

Risks, 2(4), 425-433, 2014
Number of pages: 9 Posted: 17 Apr 2014 Last Revised: 09 May 2015
Erhan Bayraktar, Yuchong Zhang and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics, University of Toronto - Department of Statistics and The University of Sydney
Downloads 66 (557,094)

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Model uncertainty, bid-ask prices for options, semi-static hedging, non-dominated collection of probability measures, Fundamental Theorem of Asset Pricing, super-hedging, robust no-arbitrage, non-redundant options

22.

Martingale Optimal Transport with Stopping

SIAM Journal on Control and Optimization, Forthcoming
Number of pages: 18 Posted: 03 Mar 2017 Last Revised: 24 Nov 2017
Erhan Bayraktar, Alexander Cox and Yavor Stoev
University of Michigan at Ann Arbor - Department of Mathematics, University of Bath and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 65 (561,585)
Citation 1

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martingale optimal transport, dynamic programming, optimal stopping, stochastic Perron method, viscosity solutions, concave envelope, distribution constraints

23.

Optimal Dividends in the Dual Model Under Transaction Costs

Insurance: Mathematics and Economics, Vol. 54, 2014
Number of pages: 22 Posted: 27 Feb 2014
Erhan Bayraktar, Andreas E. Kyprianou and Kazutoshi Yamazaki
University of Michigan at Ann Arbor - Department of Mathematics, University of Bath and Kansai University - Department of Mathematics
Downloads 64 (566,129)

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dual model, dividends, impulse control, spectrally positive Levy processes, scale functions

24.

Optimally Investing to Reach a Bequest Goal

Number of pages: 24 Posted: 05 Mar 2015 Last Revised: 26 May 2016
Erhan Bayraktar and V.R. Young
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 63 (570,608)
Citation 7

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Bequest motive, consumption, optimal investment, stochastic control

25.

Equilibrium concepts for time-inconsistent stopping problems in continuous time

To appear in Mathematical Finance
Number of pages: 19 Posted: 14 Sep 2019 Last Revised: 02 Oct 2020
Erhan Bayraktar, Jingjie Zhang and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 62 (575,065)
Citation 5

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Time-inconsistency, optimal stopping, strong equilibria, weak equilibria, mild equilibria, non-exponential discounting, subgame perfect Nash equilibrium

26.

On the Robust Optimal Stopping Problem

SIAM Journal on Control and Optimization, Vol. 52, No. 5, pp. 3135–3175, 2013
Number of pages: 50 Posted: 02 Feb 2014 Last Revised: 10 Jul 2016
Erhan Bayraktar and Song Yao
University of Michigan at Ann Arbor - Department of Mathematics and University of Pittsburgh
Downloads 61 (579,587)
Citation 6

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robust optimal stopping, zero-sum game of control and stopping, volatility uncertainty, dynamic programming principle, Snell envelope, nonlinear expectation, weak stability under pasting, path-dependent stochastic differential equations with controls

27.

No-Arbitrage and Hedging with Liquid American Options

Number of pages: 21 Posted: 28 May 2016
Erhan Bayraktar and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 60 (584,317)
Citation 2

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28.

Liquidation in Limit Order Books with Controlled Intensity

Mathematical Finance, Forthcoming, DOI: 10.1111/j.1467-9965.2012.00529.x
Number of pages: 23 Posted: 27 Jan 2014
Erhan Bayraktar and Michael Ludkovski
University of Michigan at Ann Arbor - Department of Mathematics and University of California, Santa Barbara
Downloads 58 (594,031)

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Limit order books, controlled intensity, optimal control of point processes, optimal control of queueing networks, fluid limit

29.

Analysis of a Finite State Many Player Game Using Its Master Equation

Number of pages: 36 Posted: 18 Jul 2017 Last Revised: 20 Jul 2018
Erhan Bayraktar and Asaf Cohen
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann arbor - Department of Mathematics
Downloads 57 (599,018)
Citation 4

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Game theory, Mean-field games, master equation, fluctuations, finite state control problem, Markov chains

30.

Stochastic Perron's Method for the Probability of Lifetime Ruin Problem Under Transaction Costs

SIAM Journal on Control and Optimization, 53(1), 91-113, 2015
Number of pages: 24 Posted: 30 Apr 2014 Last Revised: 09 May 2015
Erhan Bayraktar and Yuchong Zhang
University of Michigan at Ann Arbor - Department of Mathematics and University of Toronto - Department of Statistics
Downloads 57 (599,018)

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Stochastic Perron's method, singular control, probability of lifetime ruin, transaction costs, viscosity solutions, comparison principle

31.

On Zero-Sum Optimal Stopping Games

Number of pages: 8 Posted: 19 Aug 2014
Erhan Bayraktar and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 56 (604,041)
Citation 5

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Stopping games with priority, non-anticipative stopping strategies, American options

32.

Minimizing the Probability of Lifetime Drawdown Under Constant Consumption

Insurance: Mathematics and Economics, Forthcoming
Number of pages: 26 Posted: 21 May 2016
Bahman Angoshtari, Erhan Bayraktar and V.R. Young
University of Miami - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 55 (609,105)
Citation 1

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Optimal investment, stochastic optimal control, probability of drawdown

33.

Optimal Investment with Random Endowments and Transaction Costs: Duality Theory and Shadow Prices

Number of pages: 36 Posted: 15 May 2016
Erhan Bayraktar and Xiang Yu
University of Michigan at Ann Arbor - Department of Mathematics and Hong Kong Polytechnic University
Downloads 55 (609,105)
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Proportional Transaction Costs, Unbounded Random Endowments, Acceptable Portfolios, Superhedging Theorem, Utility Maximization, Shadow Prices, Convex Duality

34.

Optimal Dividend Distribution Under Drawdown and Ratcheting Constraints on Dividend Rates

SIAM J. Financial Mathematics, to appear (2019)
Number of pages: 34 Posted: 11 Jul 2018 Last Revised: 27 Mar 2019
Bahman Angoshtari, Erhan Bayraktar and V.R. Young
University of Miami - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 54 (614,350)
Citation 4

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Optimal Dividend, Drawdown Constraint, Ratcheting, Stochastic Control, Optimal Control, Variational Inequality, Free-Boundary Problem

35.

On Optimal Dividends in the Dual Model

Astin Bulletin, vol. 43, no. 3, 2013, pp 359 - 372
Number of pages: 13 Posted: 27 Feb 2014
Erhan Bayraktar, Andreas E. Kyprianou and Kazutoshi Yamazaki
University of Michigan at Ann Arbor - Department of Mathematics, University of Bath and Kansai University - Department of Mathematics
Downloads 54 (614,350)

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Dual model, dividends, capital injections, spectrally positive Levy processes, scale functions

36.

Purchasing Life Insurance to Reach a Bequest Goal

Number of pages: 30 Posted: 22 Feb 2014 Last Revised: 23 Feb 2014
Erhan Bayraktar, S. D. Promislow and V.R. Young
University of Michigan at Ann Arbor - Department of Mathematics, York University - Department of Mathematics & Statistics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 54 (614,350)

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Term life insurance, whole life insurance, bequest motive, deterministic control

37.

Estimating the Fractal Dimension of the S&P 500 Index Using Wavelet Analysis

International Journal of Theoretical and Applied Finance, Vol. 7, No. 5, 2004
Number of pages: 26 Posted: 30 May 2016
Erhan Bayraktar, H. Vincent Poor and Ronnie Sircar
University of Michigan at Ann Arbor - Department of Mathematics, Princeton University - Department of Electrical Engineering and Princeton University - Department of Operations Research and Financial Engineering
Downloads 53 (619,604)
Citation 1

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High-frequency data, S\&P 500 index, long range dependence, heavy tailed marginals, fractional Brownian motion, wavelet analysis, log scale spectrum

38.

On Arbitrage and Duality Under Model Uncertainty and Portfolio Constraints

Number of pages: 20 Posted: 13 Feb 2014
Erhan Bayraktar and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 52 (624,862)
Citation 1

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Fundamental theorem of asset pricing, sub-(super-)hedging, model uncertainty, portfolio constraints, optional decomposition

39.

Terminal Ranking Games

Forthcoming, Mathematics of Operations Research
Number of pages: 22 Posted: 27 Jun 2019 Last Revised: 22 Jun 2020
Erhan Bayraktar and Yuchong Zhang
University of Michigan at Ann Arbor - Department of Mathematics and University of Toronto - Department of Statistics
Downloads 51 (630,352)
Citation 3

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tournaments, rank-based rewards, mechanism design, mean field games, price of anarchy, Schrodinger bridges, Lorenz order

40.

Optimal Stopping for Non-Linear Expectations - Part I

Stochastic Processes and Their Applications, 121(2), 185-211, 2011
Number of pages: 22 Posted: 15 Feb 2014 Last Revised: 10 Jul 2016
Erhan Bayraktar and Song Yao
University of Michigan at Ann Arbor - Department of Mathematics and University of Pittsburgh
Downloads 51 (635,750)

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Nonlinear expectations, Optimal stopping, Snell envelope, Stability, g-expectations

41.

On an Optimal Stopping Problem of an Insider

Number of pages: 6 Posted: 23 Apr 2014
Erhan Bayraktar and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 50 (635,750)

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optimal stopping problem of an insider, Reflected Backward Stochastic Differential Equations (RBSDEs), Levy's modulus for Brownian motion

42.

Queueing Theoretic Approaches to Financial Price Fluctuations

in Handbooks in OR&MS: Financial Engineering, 15, eds. John Birge and Vadim Linetsky, (Elsevier)
Number of pages: 36 Posted: 30 May 2016
Erhan Bayraktar, Ulrich Horst and Ronnie Sircar
University of Michigan at Ann Arbor - Department of Mathematics, Humboldt University of Berlin and Princeton University - Department of Operations Research and Financial Engineering
Downloads 49 (641,298)

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43.

A Rank-Based Mean Field Game in the Strong Formulation

Electronic Communications in Probability, 21, paper no. 72, 1-12, 2016
Number of pages: 12 Posted: 13 May 2016 Last Revised: 30 Jun 2019
Erhan Bayraktar and Yuchong Zhang
University of Michigan at Ann Arbor - Department of Mathematics and University of Toronto - Department of Statistics
Downloads 49 (641,298)
Citation 2

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Mean Field Games, Competition, Common Noise, Rank-Dependent Interaction, Non-Local Interaction, Strong Formulation

44.

On the Impulse Control of Jump Diffusions

SIAM Journal on Control and Optimization, 51 (3), 2612-2637, 2013
Number of pages: 24 Posted: 25 Feb 2014
Erhan Bayraktar, Thomas Emmerling and Jose Menaldi
University of Michigan at Ann Arbor - Department of Mathematics, Zicklin School of Business, Baruch College - The City University of New York and Wayne State University
Downloads 49 (646,926)
Citation 1

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Impulse Control, PIDE, Regularity

45.

Risk Sensitive Control of the Lifetime Ruin Problem

Number of pages: 28 Posted: 22 Mar 2015
Erhan Bayraktar and Asaf Cohen
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann arbor - Department of Mathematics
Downloads 48 (646,926)

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Probability of lifetime ruin, optimal investment, risk sensitive control, large deviations, differential games

46.

Purchasing Term Life Insurance to Reach a Bequest Goal While Consuming

SIAM Journal on Finance, Forthcoming
Number of pages: 31 Posted: 02 Mar 2016
Erhan Bayraktar, S. D. Promislow and V.R. Young
University of Michigan at Ann Arbor - Department of Mathematics, York University - Department of Mathematics & Statistics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 47 (652,633)
Citation 1

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Term life insurance, bequest motive, consumption, optimal investment, stochastic control

47.

Unanticipated Features of the Multidimensional G-Normal Distribution

Number of pages: 16 Posted: 20 Jul 2014
Erhan Bayraktar and Alexander Munk
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 47 (652,633)

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sublinear expectation; multi-dimensional G-normal distribution, independence

48.

A Weak Dynamic Programming Principle for Zero-Sum Stochastic Differential Games with Unbounded Controls

SIAM Journal on Control and Optimization, 51 (3), 2036-2080, 2013
Number of pages: 42 Posted: 15 Feb 2014 Last Revised: 10 Jul 2016
Erhan Bayraktar and Song Yao
University of Michigan at Ann Arbor - Department of Mathematics and University of Pittsburgh
Downloads 45 (664,310)

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Zero-sum stochastic differential games, Elliott-Kalton strategies, weak dynamic programming principle, backward stochastic differential equations, viscosity solutions, fully non-linear PDEs.

49.

Robust Maximization of Asymptotic Growth Under Covariance Uncertainty

The Annals of Applied Probability (2013), Vol. 23, No. 5, pp. 1817–1840.
Number of pages: 25 Posted: 01 Feb 2014
Erhan Bayraktar and Yu-Jui Huang
University of Michigan at Ann Arbor - Department of Mathematics and University of Colorado at Boulder - Department of Applied Mathematics
Downloads 45 (664,310)

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asymptotic growth rate, robustness, covariance uncertainty, Pucci’s operator, principal eigenvalue for fully nonlinear elliptic operators

50.

Optimal Stopping for Dynamic Convex Risk Measures

Illinois Journal of Mathematics, 54, 1025-1067, 2010
Number of pages: 43 Posted: 16 Feb 2014 Last Revised: 08 Jul 2016
Erhan Bayraktar, Ioannis Karatzas and Song Yao
University of Michigan at Ann Arbor - Department of Mathematics, Columbia University - Department of Statistics and University of Pittsburgh
Downloads 42 (682,557)

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Convex risk measures, continuous-time optimal stopping, robustness methods, zero sum games, saddle point, reflected backward stochastic differential equations, BMO martingales

51.

Asymptotics for Small Nonlinear Price Impact: A PDE Homogenization Approach to the Multidimensional Case

To appear in Mathematical Finance.
Number of pages: 63 Posted: 02 Jan 2019 Last Revised: 24 Jun 2020
Erhan Bayraktar, Thomas Cayé and Ibrahim Ekren
University of Michigan at Ann Arbor - Department of Mathematics, Dublin City University - School of Mathematical Sciences and Florida State University
Downloads 41 (688,823)
Citation 1

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utility maximization, portfolio choice, non-linear price impact, asymptotic expansion, viscosity solutions, homogenization

52.

Valuation Equations for Stochastic Volatility Models

SIAM J. Finan. Math., 3(1), 351–373, 2012.
Number of pages: 25 Posted: 28 May 2016
Erhan Bayraktar, Constantinos Kardaras and Hao Xing
University of Michigan at Ann Arbor - Department of Mathematics, London School of Economics & Political Science (LSE) and Boston University - Questrom School of Business
Downloads 41 (688,823)

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stochastic volatility models, valuation equations, Feynman–Kac theorem, strict local martingales, necessary and sufficient conditions for uniqueness

53.

Continuity of Utility Maximization under Weak Convergence

To appear in Mathematics and Financial Economics
Number of pages: 40 Posted: 07 Nov 2018 Last Revised: 24 Jun 2020
Erhan Bayraktar, Yan Dolinsky and Jia Guo
University of Michigan at Ann Arbor - Department of Mathematics, ETH Zürich and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 38 (708,617)
Citation 1

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Incomplete Markets, Utility Maximization, Weak Convergence

54.

On the Multi-Dimensional Controller-and-Stopper Games

SIAM Journal on Control and Optimization (2013), Vol. 51, No. 2, pp. 1263-1297.
Number of pages: 35 Posted: 01 Feb 2014
Erhan Bayraktar and Yu-Jui Huang
University of Michigan at Ann Arbor - Department of Mathematics and University of Colorado at Boulder - Department of Applied Mathematics
Downloads 38 (708,617)

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controller-stopper games, weak dynamic programming principle, viscosity solutions, robust optimal stopping

55.

Quantifying an Impact of Dimensional Change in Stochastic Portfolio Theory

Number of pages: 41 Posted: 07 Mar 2023
Erhan Bayraktar, Donghan Kim and Abhishek Tilva
University of Michigan at Ann Arbor - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and Columbia University - Department of Statistics
Downloads 37 (715,253)

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functional generation, piecewise semimartingale, self-financing portfolio, stochastic dimension, stochastic portfolio theory

56.

Transport Plans with Domain Constraints

Number of pages: 21 Posted: 01 May 2018 Last Revised: 30 Aug 2019
Erhan Bayraktar, Xin Zhang and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 37 (715,253)

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Option Pricing, Strassen's Theorem, Kellerer's Theorem, Martingale optimal transport, domain constraints, bounded volatility/quadratic variation, G-expectations, Kantorovich duality, monotonicity principle

57.

Distribution-Constrained Optimal Stopping

Forthcoming in Mathematical Finance
Number of pages: 34 Posted: 08 Jul 2017 Last Revised: 30 Dec 2018
Erhan Bayraktar and Christopher Miller
University of Michigan at Ann Arbor - Department of Mathematics and University of California, Berkeley - Department of Mathematics
Downloads 37 (715,253)

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Robust hedging with a volatility outlook

58.

Strict Local Martingale Deflators and Valuing American Call-Type Options

Finance Stochastics, Vol. 16, No. 2, 2012
Number of pages: 17 Posted: 28 May 2016
Erhan Bayraktar, Constantinos Kardaras and Hao Xing
University of Michigan at Ann Arbor - Department of Mathematics, London School of Economics & Political Science (LSE) and Boston University - Questrom School of Business
Downloads 36 (722,193)

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Strict local martingales, Deflators, American call options

59.

Optimal Stopping with Random Maturity Under Nonlinear Expectations

Number of pages: 36 Posted: 21 Jul 2016
Erhan Bayraktar and Song Yao
University of Michigan at Ann Arbor - Department of Mathematics and University of Pittsburgh
Downloads 34 (736,150)
Citation 3

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discretionary stopping, random maturity, controls in weak formulation, optimal stopping, nonlinear expectation, weak stability under pasting, Lipschitz continuous stopping time, dynamic programming principle, martingale approach.

60.

Doubly Reflected BSDEs with Integrable Parameters and Related Dynkin Games

Stochastic Processes and their Applications 125 (2015) 4489–4542
Number of pages: 40 Posted: 20 Jul 2016 Last Revised: 21 Jul 2016
Erhan Bayraktar and Song Yao
University of Michigan at Ann Arbor - Department of Mathematics and University of Pittsburgh
Downloads 34 (736,150)

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BSDEs, Reflected BSDEs, Doubly reflected BSDEs, g-evaluation/expectation, Penalization, Optimal stopping problems, Pasting local solutions, Dynkin games, Saddle points.

61.

Multi-Scale Time-Changed Birth Processes for Pricing Multi-Name Credit Derivatives

Applied Mathematical Finance, Vol. 16, No. 5, 2009
Number of pages: 23 Posted: 24 Feb 2014
Erhan Bayraktar and Bo Yang
University of Michigan at Ann Arbor - Department of Mathematics and Morgan Stanley
Downloads 34 (736,150)

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Pricing multiname credit derivatives, pertubation approximation, multiple time scales, time changed birth processes, index/tranche swap, calibration

62.

Quadratic Reflected BSDEs with Unbounded Obstacles

Stochastic Processes and their Applications, 122 (4), 1155-1203, 2012
Number of pages: 60 Posted: 15 Feb 2014 Last Revised: 10 Jul 2016
Erhan Bayraktar and Song Yao
University of Michigan at Ann Arbor - Department of Mathematics and University of Pittsburgh
Downloads 33 (743,511)

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Quadratic reflected backward stochastic differential equations, concave generator, Legenre-Fenchel duality, optimal stopping problems for quadratic g-evaluations, theta-difference method, stability, obstacle problems for semi-linear parabolic PDEs, viscosity solutions.

63.

On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps

Quantitative Finance, 11 (3), 335-341, 2011.
Number of pages: 9 Posted: 02 Feb 2014
Erhan Bayraktar
University of Michigan at Ann Arbor - Department of Mathematics
Downloads 33 (743,511)

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American options, jump diffusion, smooth fit, perpetual

64.

Proving Regularity of the Minimal Probability of Ruin Via a Game of Stopping and Control

Finance Stochastics, Vol. 15, No. 4, 2011
Number of pages: 31 Posted: 28 May 2016
Erhan Bayraktar and V.R. Young
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 32 (750,925)
Citation 1

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probability of lifetime ruin, stochastic games, optimal stopping, optimal investment, viscosity solution, Hamilton-Jacobi-Bellman equation, variational inequality

65.

On the Robust Dynkin Game

Number of pages: 32 Posted: 21 Jul 2016
Erhan Bayraktar and Song Yao
University of Michigan at Ann Arbor - Department of Mathematics and University of Pittsburgh
Downloads 30 (766,177)

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robust Dynkin game, nonlinear expectation, dynamic programming principle, controls in weak formulation, weak stability under pasting, martingale approach, path-dependent stochastic di erential equations with controls, optimal triplet, optimal stopping with random maturity

66.

A Quantitative Comparison of Unemployment Benefit Extension and Level Increase

Number of pages: 30 Posted: 19 Apr 2023
Erhan Bayraktar, Indrajit Mitra and Jingjie Zhang
University of Michigan at Ann Arbor - Department of Mathematics, Federal Reserve Banks - Federal Reserve Bank of Atlanta and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 29 (773,932)

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Unemployment insurance

67.

Weak Reflection Principle for Levy Processes

Number of pages: 33 Posted: 18 Jul 2014
Erhan Bayraktar and Sergey Nadtochiy
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 29 (773,932)
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Weak reflection principle, barrier options, static hedging, Levy processes

68.

Equilibrium Transport with Time-Inconsistent Costs: An Application to Matching Problems in the Job Market

Number of pages: 47 Posted: 08 Feb 2023 Last Revised: 29 Aug 2023
Erhan Bayraktar and Bingyan Han
University of Michigan at Ann Arbor - Department of Mathematics and Department of Mathematics, University of Michigan
Downloads 28 (781,648)

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Dynamic programming, time-inconsistent costs, bicausal optimal transport, job market

69.

A Limit Theorem for Financial Markets with Inert Investors

Mathematics of Operations Research, 2006, Volume 31 (4), 789-810.
Number of pages: 25 Posted: 30 May 2016
Erhan Bayraktar, Ulrich Horst and Ronnie Sircar
University of Michigan at Ann Arbor - Department of Mathematics, Humboldt University of Berlin and Princeton University - Department of Operations Research and Financial Engineering
Downloads 28 (781,648)

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Semi-Markov processes; fractional Brownian motion; functional central limit theorem; market microstructure; investor inertia.

70.

Extended Weak Convergence and Utility Maximization with Proportional Transaction Costs

Forthcoming, Finance and Stochastics
Number of pages: 22 Posted: 24 Jul 2020
Erhan Bayraktar, Yan Dolinsky and Leonid Dolinskyi
University of Michigan at Ann Arbor - Department of Mathematics, ETH Zürich and affiliation not provided to SSRN
Downloads 27 (789,537)
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Utility Maximization, Proportional Transaction Costs, Extended Weak Convergence, Meyer--Zheng Topology

71.

Optimal Stopping for Non-Linear Expectations - Part II

Stochastic Processes and Their Applications, 121(2), 212-264, 2011
Number of pages: 38 Posted: 15 Feb 2014 Last Revised: 10 Jul 2016
Erhan Bayraktar and Song Yao
University of Michigan at Ann Arbor - Department of Mathematics and University of Pittsburgh
Downloads 27 (789,537)
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Nonlinear expectations, Optimal stopping, Snell envelope, Stability, g-expectations

72.

On Controller-Stopper Problems with Jumps and Their Applications to Indifference Pricing of American Options

Siam Journal of Financial Math, Vol. 5, pp. 20-49, 2013
Number of pages: 29 Posted: 07 Feb 2014
Erhan Bayraktar and Zhou Zhou
University of Michigan at Ann Arbor - Department of Mathematics and The University of Sydney
Downloads 27 (789,537)
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controller-stopper problems, jumps, decomposition, indifference pricing, American options, RBSDEs

73.

Minimizing the Expected Lifetime Spent in Drawdown Under Proportional Consumption

Finance Research Letters, Forthcoming
Number of pages: 12 Posted: 25 Aug 2015 Last Revised: 26 Aug 2015
Bahman Angoshtari, Erhan Bayraktar and V.R. Young
University of Miami - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 26 (797,622)

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Drawdown, occupation time, optimal investment, stochastic control, free-boundary problem

74.

Optimal Consumption under a Habit-Formation Constraint: The Deterministic Case

Number of pages: 43 Posted: 31 Oct 2022
Bahman Angoshtari, Erhan Bayraktar and V.R. Young
University of Miami - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 25 (805,897)

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Addictive habit formation, consumption hump, optimal consumption, average past consumption, optimal control, free-boundary problem

75.

A Neural Network Approach to High-Dimensional Optimal Switching Problems with Jumps in Energy Markets

Number of pages: 24 Posted: 19 Oct 2022
Erhan Bayraktar, Asaf Cohen and April Nellis
University of Michigan at Ann Arbor - Department of Mathematics, University of Michigan at Ann arbor - Department of Mathematics and University of Michigan
Downloads 24 (814,341)

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Deep neural networks, forward-backward systems of stochastic differential equations, optimal switching, Monte Carlo algorithm, optimal investment in power generation, planning problems

76.

Optimal Consumption Under a Habit-Formation Constraint

Number of pages: 35 Posted: 12 May 2021 Last Revised: 02 Aug 2022
Bahman Angoshtari, Erhan Bayraktar and V.R. Young
University of Miami - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 23 (823,040)

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Addictive habit formation, consumption hump, optimal consumption, average past consumption, optimal control, free-boundary problem

77.

Correspondence between Lifetime Minimum Wealth and Utility of Consumption

Finance Stochastics, Vol. 11, 2007
Number of pages: 24 Posted: 28 May 2016
Erhan Bayraktar and V.R. Young
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 20 (849,607)

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Optimal control, Probability of ruin, Utility of consumption, Investment/consumption decisions

78.

Data-Driven Nonparametric Robust Control under Dependence Uncertainty

Number of pages: 25 Posted: 24 Oct 2022
Erhan Bayraktar and Tao Chen
University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan
Downloads 17 (877,451)

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nonparametric adaptive robust control, model uncertainty, stochastic control, adaptive robust dynamic programming, Wasserstein distance, Markovian control problem, utility maximization, copula, machine learning, stochastic gradient descent ascent

79.

Optimal Investment and Consumption under a Habit-Formation Constraint

“Optimal Investment and Consumption under a Habit-Formation Constraint,” with Erhan Bayraktar and Virginia Young, SIAM Journal on Financial Mathematics, 13(1):321–352, 2022.
Number of pages: 31 Posted: 01 Nov 2022
Bahman Angoshtari, Erhan Bayraktar and V.R. Young
University of Miami - Department of Mathematics, University of Michigan at Ann Arbor - Department of Mathematics and University of Michigan at Ann Arbor - Department of Mathematics
Downloads 14 (906,286)

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Optimal investment and consumption, habit formation, habit persistence, average past consumption, stochastic control, free-boundary problem

80.

A Rank-Based Reward between a Principal and a Field of Agents: Application to Energy Savings

Number of pages: 32 Posted: 24 Oct 2022 Last Revised: 31 Jul 2023
Clemence Alasseur, Erhan Bayraktar, Roxana Dumitrescu and Quentin JACQUET
Électricité de France (EDF), University of Michigan at Ann Arbor - Department of Mathematics, King’s College London and Electricite de France
Downloads 11 (935,611)

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Ranking games, Principal-Agent problem, Mean-field games, Energy savings