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

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  • Moussa Kounta

    (University of The Bahamas)

  • Nathan J. Dawson

    (Hawaii Pacific University
    Hawaii Pacific University
    Washington State University)

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.

Suggested Citation

  • Moussa Kounta & Nathan J. Dawson, 2021. "Linear Quadratic Gaussian Homing for Markov Processes with Regime Switching and Applications to Controlled Population Growth/Decay," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 1155-1172, September.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:3:d:10.1007_s11009-020-09800-2
    DOI: 10.1007/s11009-020-09800-2
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    References listed on IDEAS

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    1. L. Ferrante & S. Bompadre & L. Possati & L. Leone, 2000. "Parameter Estimation in a Gompertzian Stochastic Model for Tumor Growth," Biometrics, The International Biometric Society, vol. 56(4), pages 1076-1081, December.
    2. Lu, Yi & Li, Shuanming, 2005. "On the probability of ruin in a Markov-modulated risk model," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 522-532, December.
    3. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
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    Cited by:

    1. Mario Lefebvre, 2023. "A Discrete-Time Homing Problem with Two Optimizers," Games, MDPI, vol. 14(6), pages 1-10, October.

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