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

作　　者：史敬涛 吴臻 

机构地区：[1]School of Mathematics, Shandong University

出　　处：《Acta Mathematica Scientia》2011年第2期419-433,共15页数学物理学报（B辑英文版）

基　　金：supported by the National Basic Research Program of China (973 Program, 2007CB814904);the National Natural Science Foundations of China (10921101);Shandong Province (2008BS01024, ZR2010AQ004);the Science Funds for Distinguished Young Scholars of Shandong Province (JQ200801);Shandong University (2009JQ004),the Independent Innovation Foundations of Shandong University (IIFSDU,2009TS036, 2010TS060)

摘　　要：A stochastic maximum principle for the risk-sensitive optimal control prob- lem 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.A stochastic maximum principle for the risk-sensitive optimal control prob- lem 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 adioint equation 

分 类 号：O232[理学—运筹学与控制论] O211.6[理学—数学]