Journal of Optimization Theory and Applications

, Volume 163, Issue 2, pp 614–641 | Cite as

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

  • Ruihua LiuEmail author


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.


Optimal investment and consumption problem Transaction cost Regime-switching model Hamilton-Jacobi-Bellman equation Power utility 



The author would like to thank the two anonymous referees and the editors for their valuable comments, which helped to improve the exposition of this paper.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of DaytonDaytonUSA

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