关于带跳的反射扩散过程的随机最优控制问题

A Note on Stochastic Optimal Control of Reflected Diffusions With Jumps

1.
Department of Mathematics, Zhongshan University, Guangzhou 510725, P R China;
2.
Faculty of Science and Technology, University of Macau, P O Box 3001. Macau, P R China

摘要: 研究一类半空间上带泊松跳的反射扩散过程的随机最优控制问题。得到关于这一控制问题的非线性Nisio半群,和联系这一半群的带Neumann边界条件的哈密顿。雅可比。贝尔曼方程。讨论这一类方程的粘性解的存在唯一性等问题。证明该控制问题中的价值函数是这一方程的一个粘性解。
- 随机最优控制 /
- 带跳反射扩散 /
- 哈密顿雅可比贝尔曼方程 /
- 粘性解
Abstract: Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered.The nonlinear Nisio.s semigro up for such optimal control problems was constructed.A Hamilton-Jaco bi-Bellman equation with the Ne umann boundary condition associated with this semigroup was o btained.Then,visco sity solutions of this equation were defined and discussed,and various uniqueness of this equation was also considered.Finally,the value function in such optimal control problems is shown to be a viscosity solution of this equation.
- stochastic optimal control /
- reflected diffusion with jumps /
- Hamilton-Jacobi-Bellman equation /
- viscosity solution

[1]	Lions P L. Optimal control of reflected diffusion processes[J]. Lect Notes in Control and Inf Sci,1983,61:157-163.
[2]	Menaldi J L, Robin M. construction and control of reflected diffusion with jumps[J]. Lect Notes in Control and Inf Sci,1983,69:309-322.
[3]	Maurel M C, Karoui N E, Marchal B. Reflexiom discontinue et systemes stochastiques[J]. Ann Probab,1980,8(3):1047-1067.
[4]	丁灯. 关于带跳反射扩散过程的下鞅问题及其应用[J]. 中山大学学报(自然科学版),1995,34(2):7-13.
[5]	Lions P L, Menaldi J L. Optimal control of stochastic integrals and Hamilton-Jacobi-Bellman equations, Parts 1 and 2[J]. SIAM J Control Optim,1980,20(1):58-95.
[6]	Krylov N V. Controlled Diffusion Processes[M]. Berlin: Springer,1985.
[7]	Nisio M. Lectures on Stochastic Control Theory[M]. Macmillan India Limited,1981.
[8]	Ikeda N, Watanabe S. Stochastic Differential Equations and Diffusion Processes[M]. Tokyo: North-Holland Publishing Compang,1981.
[9]	Krylov N V, Pragarauskas H. On the Bellman equations for uniformly non-degenerated general stochastic processes[J]. Liet Matem Rink,1980,20(1):85-95.