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Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (9): 1079-1090.

• 论文 • 上一篇    下一篇

A NOTE ON STOCHASTIC OPTIMAL CONTROL OF REFLECTED DIFFUSIONS WITH JUMPS

丁灯1,2   

  1. 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
  • 收稿日期:1999-04-06 修回日期:2000-04-16 出版日期:2000-09-18 发布日期:2000-09-18

A NOTE ON STOCHASTIC OPTIMAL CONTROL OF REFLECTED DIFFUSIONS WITH JUMPS

DING Deng1,2   

  1. 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
  • Received:1999-04-06 Revised:2000-04-16 Online:2000-09-18 Published:2000-09-18

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被引次数

2

摘要： Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio’s semigroup for such optimal control problems was constructed. A Hamilton-Jacobi-Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function was such optimal control problems is shown to be a viscosity solution of this equation.

Abstract: Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio’s semigroup for such optimal control problems was constructed. A Hamilton-Jacobi-Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function was such optimal control problems is shown to be a viscosity solution of this equation.

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