On the Uniqueness of Unbounded Viscosity Solutions Arising in an Optimal Terminal Wealth Problem with Transaction Costs

SIAM Journal on Control and Optimization, Vol. 53, No. 5, pp. 2878-2897, 2015.

Posted: 23 Aug 2013 Last revised: 3 May 2016

See all articles by Christoph Belak

Christoph Belak

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

Olaf Menkens

Dublin City University - School of Mathematical Sciences

Jörn Sass

University of Kaiserslautern - Department of Mathematics

Date Written: March 5, 2015

Abstract

We study the uniqueness of viscosity solutions of a Hamilton-Jacobi-Bellman equation which arises in a portfolio optimization problem in which an investor maximizes expected utility of terminal wealth in the presence of proportional transaction costs. Our main contribution is that the comparison theorem can be applied to prove the uniqueness of the value function in the portfolio optimization problem for logarithmic and power utility.

Keywords: unbounded viscosity solutions, comparison principle, optimal terminal wealth, transaction costs

Suggested Citation

Belak, Christoph and Menkens, Olaf and Sass, Jörn, On the Uniqueness of Unbounded Viscosity Solutions Arising in an Optimal Terminal Wealth Problem with Transaction Costs (March 5, 2015). SIAM Journal on Control and Optimization, Vol. 53, No. 5, pp. 2878-2897, 2015., Available at SSRN: https://ssrn.com/abstract=2314445 or http://dx.doi.org/10.2139/ssrn.2314445

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

Olaf Menkens

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

Jörn Sass

University of Kaiserslautern - Department of Mathematics ( email )

D-67653 Kaiserslautern
Germany

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
597
PlumX Metrics