Linear Quadratic Gaussian Homing for Markov Processes with Regime Switching and Applications to Controlled Population Growth/Decay

Moussa Kounta () and Nathan J. Dawson ()
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Moussa Kounta: University of The Bahamas
Nathan J. Dawson: Hawaii Pacific University

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 3, 1155-1172

Abstract: Abstract The problem of optimally controlling one-dimensional diffusion processes until they enter a given stopping set is extended to include Markov regime switching. The optimal control problem is presented by making use of dynamic programming. In the case where the Markov chain has two states, the optimal homotopy analysis method (OHAM) is used to obtain an analytical approximation of the value function, which is compared to the finite difference approximation with successive updates of the nonlinear and coupling terms. As an example, the method is applied to controlled population growth with regime switching.

Keywords: Markov chain; Regime switching; Optimal homotopy analysis method; Linear quadratic Gaussian; Optimal control; Viscosity solution; MSC 49; MSC 60; MSC 65 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-020-09800-2

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