2020/07/03 by Hidekazu Yoshioka, H. Yoshioka, Yoshioka, H. +3
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Electrical engineering #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.OC
paper · pdf · doi:10.48550/arxiv.2007.01457
arxiv created 2020/07/03 · openalex publication_date 2020/07/03 · arxiv updated 2020/07/06 · openalex created_date 2020/07/10 · openalex updated_date 2026/07/28
The objectives and contributions of this paper are mathematical and numerical analyses of a stochastic control problem of bounded population dynamics under ambiguity, an important but not well-studied problem, focusing on the optimality equation as a nonlinear degenerate parabolic partial integro-differential equation (PIDE). The ambiguity comes from lack of knowledge on the continuous and jump noises in the dynamics, and its optimization appears as nonlinear and nonlocal terms in the PIDE. Assuming a strong dynamic programming principle for continuous value functions, we characterize its solutions from both viscosity and distribution viewpoints. Numerical computation focusing on an ergodic case are presented as well to complement the mathematical analysis.