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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
Article

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.

Keywords

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

Notes

Acknowledgements

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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