Regular finite fuel stochastic control problems with exit time

2015/01/29 by Dmitry B. Rokhlin, Rokhlin, Dmitry B., Georgii Mironenko +1
Economics, Econometrics and Finance · Mathematics · #49L25 #49N90 #93B40 #93E20 #Climate Change Policy and Economics #FOS: Mathematics #Mathematical Biology Tumor Growth #Optimization and Control (math.OC) #Probability (math.PR) #Stochastic processes and financial applications #math.OC #math.PR #msc:49L25 #msc:49N90 #msc:93B40 #msc:93E20

paper · pdf · doi:10.48550/arxiv.1501.07437

19 pages, 7 figures

arxiv created 2015/01/29 · openalex publication_date 2015/01/29 · arxiv updated 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a class of exit time stochastic control problems for diffusion processes with discounted criterion, where the controller can utilize a given amount of resource, called "fuel". In contrast to the vast majority of existing literature, concerning the "finite fuel" problems, it is assumed that the intensity of fuel consumption is bounded. We characterize the value function of the optimization problem as the unique continuous viscosity solution of the Dirichlet boundary value problem for the correspondent Hamilton-Jacobi-Bellman (HJB) equation. Our assumptions concern the HJB equations, related to the problems with infinite fuel and without fuel. Also, we present computer experiments, for the problems of optimal regulation and optimal tracking of a simple stochastic system with the stable or unstable equilibrium point.

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