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Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model

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  • Ruihua Liu

    (University of Dayton)

Abstract

This paper is concerned with an infinite-horizon problem of optimal investment and consumption with proportional transaction costs in continuous-time regime-switching models. An investor distributes his/her wealth between a stock and a bond and consumes at a non-negative rate from the bond account. The market parameters (the interest rate, the appreciation rate, and the volatility rate of the stock) are assumed to depend on a continuous-time Markov chain with a finite number of states (also known as regimes). The objective of the optimization problem is to maximize the expected discounted total utility of consumption. We first show that for a class of hyperbolic absolute risk aversion utility functions, the value function is a viscosity solution of the Hamilton–Jacobi–Bellman equation associated with the optimization problem. We then treat a power utility function and generalize the existing results to the regime-switching case.

Suggested Citation

  • Ruihua Liu, 2014. "Optimal Investment and Consumption with Proportional Transaction Costs in Regime-Switching Model," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 614-641, November.
    • Handle: RePEc:spr:joptap:v:163:y:2014:i:2:d:10.1007_s10957-013-0445-y
    DOI: 10.1007/s10957-013-0445-y
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    References listed on IDEAS

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    1. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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    Cited by:

    1. Zbigniew Palmowski & {L}ukasz Stettner & Anna Sulima, 2018. "Optimal portfolio selection in an It\^o-Markov additive market," Papers 1806.03496, arXiv.org.
    2. Yuhang Zhen, 2024. "Approximations of the Euler–Maruyama Method of Stochastic Differential Equations with Regime Switching," Mathematics, MDPI, vol. 12(12), pages 1-17, June.
    3. Zbigniew Palmowski & Łukasz Stettner & Anna Sulima, 2019. "Optimal Portfolio Selection in an Itô–Markov Additive Market," Risks, MDPI, vol. 7(1), pages 1-32, March.

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