Finite-Horizon Optimal Investment with Transaction Costs: Construction of the Optimal Strategies

27 Pages Posted: 28 Jul 2015 Last revised: 7 May 2018

See all articles by Christoph Belak

Christoph Belak

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

Jörn Sass

University of Kaiserslautern - Department of Mathematics

Date Written: May 2, 2018

Abstract

We revisit the problem of maximizing expected utility of terminal wealth in a Black-Scholes market with proportional transaction costs. While it is known that the value function of this problem is the unique viscosity solution of the HJB equation and that the HJB equation admits a classical solution on a reduced state space, it has been an open problem to verify that these two coincide. We establish this result by devising a verifcation procedure based on superharmonic functions. In the process, we construct optimal strategies and provide a detailed analysis of the regularity of the value function.

Keywords: Utility Maximization, Transaction Costs, Reflected Diffusions, Superharmonic Functions

JEL Classification: G11, C61

Suggested Citation

Belak, Christoph and Sass, Jörn, Finite-Horizon Optimal Investment with Transaction Costs: Construction of the Optimal Strategies (May 2, 2018). Available at SSRN: https://ssrn.com/abstract=2636341 or http://dx.doi.org/10.2139/ssrn.2636341

Christoph Belak (Contact Author)

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

Institut fur Mathematik, Sekr. MA 6-1
Strasse des 17. Juni 136
Berlin, 10623
Germany

Jörn Sass

University of Kaiserslautern - Department of Mathematics ( email )

D-67653 Kaiserslautern
Germany

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