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Stochastic Differential Games with Multiple Modes and Applications to Portfolio Optimization

Basu, Arnab and Ghosh, Mrinal K (2007) Stochastic Differential Games with Multiple Modes and Applications to Portfolio Optimization. In: Stochastic Analysis and Applications, 25 (4). pp. 845-867.

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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: Journal Article
Additional Information: Copyright of this article belongs to Taylor and Francis.
Keywords: HJI equations; Portfolio optimization; Switching diffusion processes; Value functions; Viscosity solutions.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 04 Mar 2008
Last Modified: 27 Aug 2008 13:13
URI: http://eprints.iisc.ernet.in/id/eprint/13221

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