A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS

doi:10.1016/S0252-9602(11)60242-7

Abstract

Abstract:

A stochastic maximum principle for the risk-sensitive optimal control problem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.

Key words: Risk-sensitive control, jump diffusions, maximum principle, adjoint equation

CLC Number:

93E20

SHI Jing-Tao, WU Zhen. A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS[J].Acta mathematica scientia,Series B, 2011, 31(2): 419-433.

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A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS

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