Stochastic differential games with multiple modes and applications to portfolio optimization

Document Type

Article

Publication Title

Stochastic Analysis and Application

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.

Publication Date

1-4-2007

Publisher

Taylor and Francis

Volume

Vol.25

Issue

Iss.4

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