On the uniqueneß of unbounded viscosity solutions arising in an optimal terminal wealth problem with transaction costs

Christoph Belak; Olaf Menkens; Jörn Saß

doi:10.1137/130934234

On the uniqueneß of unbounded viscosity solutions arising in an optimal terminal wealth problem with transaction costs

Christoph Belak, Olaf Menkens, Jörn Saß

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

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.

Original language	English
Pages (from-to)	2878-2897
Number of pages	20
Journal	SIAM Journal on Control and Optimization
Volume	53
Issue number	5
DOIs	https://doi.org/10.1137/130934234
State	Published - 2015
Externally published	Yes

Keywords

Comparison principle
Optimal terminal wealth
Transaction costs
Unbounded viscosity solutions

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10.1137/130934234

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abstract = "We study the uniquene{\ss} 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 uniquene{\ss} of the value function in the portfolio optimization problem for logarithmic and power utility.",

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AU - Menkens, Olaf

AU - Saß, Jörn

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AB - 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.

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KW - Transaction costs

KW - Unbounded viscosity solutions

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On the uniqueneß of unbounded viscosity solutions arising in an optimal terminal wealth problem with transaction costs

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Keywords

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