A Stochastic Recursive Optimal Control Problem Under the G-expectation Framework
A Stochastic Recursive Optimal Control Problem Under the G-expectation Framework
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DOI：
10.1007/s00245-014-9242-8
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发表时间：
2014-02
影响因子：
1.8
通讯作者：
Mingshang Hu;Shaolin Ji;Shuzhen Yang
中科院分区：
文献类型：
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作者：
Mingshang Hu;Shaolin Ji;Shuzhen Yang
本文研究了一个随机递归最优控制问题，其中目标泛函由一个由布朗运动驱动的倒向随机微分方程解来描述。在标准假设下，建立了-期望框架下的动态规划原理和相应的Hamilton-Jacobi-Bellman(HJB)方程。最后，我们证明了值函数就是所得到的HJB方程的粘性解。
In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by-Brownian motion. Under standard assumptions, we establish the dynamic programming principle and the related Hamilton–Jacobi–Bellman (HJB) equation in the framework of-expectation. Finally, we show that the value function is the viscosity solution of the obtained HJB equation.