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

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

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 419-433.doi: 10.1016/S0252-9602(11)60242-7

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

史敬涛|吴臻

School of Mathematics, Shandong University, Jinan 250100, China

收稿日期:2008-02-25 修回日期:2008-10-05 出版日期:2011-03-20 发布日期:2011-03-20
基金资助:
This work was supported by the National Basic Research Program of China (973 Program, 2007CB814904), the National Natural Science Foundations of China (10921101) and Shandong Province (2008BS01024, ZR2010AQ004), the Science Funds for Distinguished Young Scholars of Shandong Province (JQ200801) and Shandong University (2009JQ004), and the Independent Innovation Foundations of Shandong University (IIFSDU, 2009TS036, 2010TS060)

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

SHI Jing-Tao, WU Zhen

School of Mathematics, Shandong University, Jinan 250100, China

Received:2008-02-25 Revised:2008-10-05 Online:2011-03-20 Published:2011-03-20
Supported by:
This work was supported by the National Basic Research Program of China (973 Program, 2007CB814904), the National Natural Science Foundations of China (10921101) and Shandong Province (2008BS01024, ZR2010AQ004), the Science Funds for Distinguished Young Scholars of Shandong Province (JQ200801) and Shandong University (2009JQ004), and the Independent Innovation Foundations of Shandong University (IIFSDU, 2009TS036, 2010TS060)

摘要/Abstract

摘要：

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.

关键词: Risk-sensitive control, jump diffusions, maximum principle, adjoint equation

Abstract:

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

中图分类号:

93E20

史敬涛, 吴臻. A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS[J]. 数学物理学报(英文版), 2011, 31(2): 419-433.

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

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

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