Table of Contents

Large-Scale Loan Portfolio Selection

Justin Sirignano, Stanford University - Management Science & Engineering
Gerry Tsoukalas, University of Pennsylvania - The Wharton School, Stanford University
Kay Giesecke, Stanford University - Management Science & Engineering

Modeling Stock Price Dynamics with Fuzzy Opinion Networks

Li-Xin Wang, Xian Jiaotong University, Department of Automation Science and Technology

The Analysis and Computations in Determining a Financial Proxy Corresponding to De-Trending

Siya Goodwill Chule, DUT Research and Postgraduate Support
Marie de Beer, Durban University of Technology
Sibusiso Moyo, Independent


FINANCIAL ENGINEERING eJOURNAL

"Large-Scale Loan Portfolio Selection" Free Download

JUSTIN SIRIGNANO, Stanford University - Management Science & Engineering
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GERRY TSOUKALAS, University of Pennsylvania - The Wharton School, Stanford University
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KAY GIESECKE, Stanford University - Management Science & Engineering
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We consider the problem of optimally selecting a large portfolio of risky loans, such as mortgages, credit cards, auto loans, student loans, or business loans. Examples include loan portfolios held by financial institutions and fixed-income investors as well as pools of loans backing mortgage- and asset-backed securities. The size of these portfolios can range from the thousands to even hundreds of thousands. Optimal portfolio selection requires the solution of a high-dimensional nonlinear integer program and is extremely computationally challenging. For larger portfolios, this optimization problem is intractable. We propose an approximate optimization approach that yields an asymptotically optimal portfolio for a broad class of data-driven models of loan delinquency and prepayment. We prove that the asymptotically optimal portfolio converges to the optimal portfolio as the portfolio size grows large. Numerical case studies using actual loan data demonstrate its computational efficiency. The asymptotically optimal portfolio's computational cost does not increase with the size of the portfolio. It is typically many orders of magnitude faster than nonlinear integer program solvers while also being highly accurate even for moderate-sized portfolios. Our method allows for tractable, large-scale data-driven optimization of loan portfolios and could also be applicable to large-scale optimization problems for stochastic systems in other areas.

"Modeling Stock Price Dynamics with Fuzzy Opinion Networks" Free Download

LI-XIN WANG, Xian Jiaotong University, Department of Automation Science and Technology
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We propose a mathematical model for the word-of-mouth communications among stock investors through social networks and explore how the changes of the investors’ social networks influence the stock price dynamics. First, we use a Gaussian fuzzy set to model the stock price expectation of an investor, where the center and the standard deviation of the Gaussian fuzzy set represent the expected price and the uncertainty about the expected price, respectively. Then, based on a similarity measure between Gaussian fuzzy sets, we propose a bounded confidence fuzzy opinion network (BCFON) to model the social connection of investors, where only those investors whose stock price expectations are close to each other are connected, and the investors in a connected group update their fuzzy expectations as weighted averages of the previous fuzzy expectations of their neighbors. Finally, the fuzzy expectations from the BCFON are used as inputs to drive the stock price dynamics. Simulations of the price dynamic models show the details of how the topological changes of the investor networks influence the moves of the stock prices, and some common phenomena in real stock prices, such as excess volatility and trend shifting, are observed in the simulated price series and can be easily explained in our model framework. We give rigorous mathematical proofs for the convergence properties of the BCFON.

"The Analysis and Computations in Determining a Financial Proxy Corresponding to De-Trending" Free Download

SIYA GOODWILL CHULE, DUT Research and Postgraduate Support
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MARIE DE BEER, Durban University of Technology
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SIBUSISO MOYO, Independent

The purpose of this paper is to analyse the system dynamics of the trading strategy called the mixed-mix portfolio for effective utility of the strategy. The focus is on the impact of the volatility in the financial growth and transaction costs under this portfolio strategy. In addition we justify and design a system that sufficiently utilizes the presence of volatility. A counter intuitive dynamical system approach is considered to counter the unrealised infinitesimal rates based on the financial engineered foundation on how to render a stochastic process to a stationary process.

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