Acta mathematica scientia, Series B >
A RISK-SENSITIVE STOCHASTIC MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF JUMP DIFFUSIONS AND ITS APPLICATIONS
Received date: 2008-02-25
Revised date: 2008-10-05
Online 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)
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.
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 . DOI: 10.1016/S0252-9602(11)60242-7
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