Regular finite fuel stochastic control problems with exit time

Dmitry B. Rokhlin () and Georgii Mironenko
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Dmitry B. Rokhlin: Southern Federal Univeristy
Georgii Mironenko: Southern Federal Univeristy

Mathematical Methods of Operations Research, 2016, vol. 84, issue 1, No 5, 105-127

Abstract: 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 correction and optimal tracking of a simple stochastic system with the stable or unstable equilibrium point.

Keywords: Finite fuel; Exit time; Viscosity solution; Optimal correction; Optimal tracking; 93E20; 49L25; 49N90; 93B40 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s00186-016-0536-2

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