Maximum Principle for General Controlled Systems Driven by Fractional Brownian Motions

被引:0
作者
Yuecai Han
Yaozhong Hu
Jian Song
机构
[1] Jilin University,School of Mathematics
[2] University of Kansas,Department of Mathematics
[3] Rutgers University,Department of Mathematics
来源
Applied Mathematics & Optimization | 2013年 / 67卷
关键词
Stochastic optimal control; Backward differential equations; Maximum principle; Fractional Brownian motions; Controlled stochastic differential systems driven by fractional Brownian motions; Malliavin calculus; Partial information stochastic control;
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摘要
We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter H>1/2). This maximum principle specifies a system of equations that the optimal control must satisfy (necessary condition for the optimal control). This system of equations consists of a backward stochastic differential equation driven by both fractional Brownian motions and the corresponding underlying standard Brownian motions. In addition to this backward equation, the maximum principle also involves the Malliavin derivatives. Our approach is to use conditioning and Malliavin calculus. To arrive at our maximum principle we need to develop some new results of stochastic analysis of the controlled systems driven by fractional Brownian motions via fractional calculus. Our approach of conditioning and Malliavin calculus is also applied to classical system driven by standard Brownian motions while the controller has only partial information. As a straightforward consequence, the classical maximum principle is also deduced in this more natural and simpler way.
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页码:279 / 322
页数:43
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