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

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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

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.

2010 MSC Number: 

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