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Linear quadratic Gaussian homing for Markov processes with regime switching and applications to controlled population growth/decay. (English) Zbl 1475.93117

Summary: 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.

MSC:

93E20 Optimal stochastic control
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
49N10 Linear-quadratic optimal control problems
60G40 Stopping times; optimal stopping problems; gambling theory
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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