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A generalized stochastic control problem of bounded noise process under ambiguity arising in biological management

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Document pages: 32 pages

Abstract: The objectives and contributions of this paper are mathematical and numericalanalyses of a stochastic control problem of bounded population dynamics underambiguity, an important but not well-studied problem, focusing on theoptimality equation as a nonlinear degenerate parabolic partialintegro-differential equation (PIDE). The ambiguity comes from lack ofknowledge on the continuous and jump noises in the dynamics, and itsoptimization appears as nonlinear and nonlocal terms in the PIDE. Assuming astrong dynamic programming principle for continuous value functions, wecharacterize its solutions from both viscosity and distribution viewpoints.Numerical computation focusing on an ergodic case are presented as well tocomplement the mathematical analysis.

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