Convergence of Optimal Investment Problems in the Vanishing Fixed Cost Limit

29 Pages Posted: 2 Feb 2022

See all articles by Erhan Bayraktar

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Christoph Belak

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften

Frank Thomas Seifried

University of Trier

Sören Christensen

Gothenburg University

Date Written: November 26, 2021

Abstract

We consider an optimal investment problem for an investor facing both constant and proportional transaction costs and study the limit as the constant cost tends to zero. Combining the stochastic Perron's method with stability arguments for viscosity solutions, we show that the value function converges to the value function of the problem with purely proportional costs. Moreover, using a Komlos-type argument, we show that forward-convex combinations of the optimal strategies in the problem with constant costs converge to an optimal strategy for the problem without a constant cost.

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

Suggested Citation

Bayraktar, Erhan and Belak, Christoph and Seifried, Frank Thomas and Christensen, Sören, Convergence of Optimal Investment Problems in the Vanishing Fixed Cost Limit (November 26, 2021). Available at SSRN: https://ssrn.com/abstract=3972366 or http://dx.doi.org/10.2139/ssrn.3972366

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Christoph Belak (Contact Author)

Technische Universität Berlin (TU Berlin) - Fakultat II - Mathematik und Naturwissenschaften ( email )

Institut fur Mathematik, Sekr. MA 7-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

Frank Thomas Seifried

University of Trier ( email )

Department IV - Mathematics
Universitätsring 19
Trier, 54296
Germany

HOME PAGE: http://sites.google.com/site/seifriedfinance/

Sören Christensen

Gothenburg University ( email )

Göteborg, 41296
Sweden

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