Optimal investment-consumption strategy in a discrete-time model with regime switching

Ka Chun Cheung; Hailiang Yang

doi:10.3934/dcdsb.2007.8.315

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2007, Volume 8, Issue 2: 315-332. Doi: 10.3934/dcdsb.2007.8.315

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Optimal investment-consumption strategy in a discrete-time model with regime switching

Ka Chun Cheung^1, and
Hailiang Yang^2,

1.
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB, T3A, 2E2
2.
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong

Received: April 30, 2006

Revised: February 28, 2007

Published: August 2007

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Abstract

This paper analyzes the investment-consumption problem of a risk averse investor in discrete-time model. We assume that the return of a risky asset depends on the economic environments and that the economic environments are ranked and described using a Markov chain with an absorbing state which represents the bankruptcy state. We formulate the investor's decision as an optimal stochastic control problem. We show that the optimal investment strategy is the same as that in Cheung and Yang [5], and a closed form expression of the optimal consumption strategy has been obtained. In addition, we investigate the impact of economic environment regime on the optimal strategy. We employ some tools in stochastic orders to obtain the properties of the optimal strategy.

Keywords:

Optimal investment-consumption strategy,
Bankruptcy risk,
Dynamic programming,
Bellman equation,
Stochastically monotone,
Second-order stochastic dominance,
Recovery rate.

Mathematics Subject Classification: Primary: 91B28; Secondary: 90C39, 49L20.

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