Stochastic differential games with multiple modes and applications to portfolio optimization

Basu, Arnab ; Ghosh, Mrinal K. (2007) Stochastic differential games with multiple modes and applications to portfolio optimization Stochastic Analysis and Applications, 25 (4). pp. 845-867. ISSN 0736-2994

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Related URL: http://dx.doi.org/10.1080/07362990701420126

Abstract

We study a zero-sum stochastic differential game with multiple modes. The state of the system is governed by "controlled switching" diffusion processes. Under certain conditions, we show that the value functions of this game are unique viscosity solutions of the appropriate Hamilton-Jacobi-Isaac' system of equations. We apply our results to the analysis of a portfolio optimization problem where the investor is playing against the market and wishes to maximize his terminal utility. We show that the maximum terminal utility functions are unique viscosity solutions of the corresponding Hamilton-Jacobi-Isaac' system of equations.

Item Type:Article
Source:Copyright of this article belongs to Taylor and Francis Ltd.
Keywords:HJI Equations; Portfolio Optimization; Switching Diffusion Processes; Value Functions; Viscosity Solutions
ID Code:11947
Deposited On:13 Nov 2010 13:31
Last Modified:02 Jun 2011 07:41

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