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A note on strochastic optimal control of reflected diffusions with jumps

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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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Authors and Affiliations

  1. Department of Mathematics, Zhongshan University, 510725, Guangzhou, P R China

    Ding Deng Assistant Professor, Doctor

  2. Faculty of Science and Technology, University of Macau, P O Box 3001, Macau, P R China

    Ding Deng Assistant Professor, Doctor

Authors
  1. Ding Deng Assistant Professor, Doctor
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Communicated by XUE Da-wei

Biography

DING Deng (1959≈)

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Deng, D. A note on strochastic optimal control of reflected diffusions with jumps. Appl Math Mech 21, 1079–1090 (2000). https://doi.org/10.1007/BF02459319

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  • DOI: https://doi.org/10.1007/BF02459319

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