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An optimal investment and consumption model with stochastic returns

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  • Xikui Wang
  • Yanqing Yi

Abstract

We consider a financial market consisting of a risky asset and a riskless one, with a constant or random investment horizon. The interest rate from the riskless asset is constant, but the relative return rate from the risky asset is stochastic with an unknown parameter in its distribution. Following the Bayesian approach, the optimal investment and consumption problem is formulated as a Markov decision process. We incorporate the concept of risk aversion into the model and characterize the optimal strategies for both the power and logarithmic utility functions with a constant relative risk aversion (CRRA). Numerical examples are provided that support the intuition that a higher proportion of investment should be allocated to the risky asset if the mean return rate on the risky asset is higher or the risky asset return rate is less volatile. Copyright © 2008 John Wiley & Sons, Ltd.

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  • Xikui Wang & Yanqing Yi, 2009. "An optimal investment and consumption model with stochastic returns," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(1), pages 45-55, January.
    • Handle: RePEc:wly:apsmbi:v:25:y:2009:i:1:p:45-55
    DOI: 10.1002/asmb.720
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    Cited by:

    1. You Liang & Xikui Wang & Yanqing Yi, 2013. "One-armed bandit process with a covariate," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 993-1006, October.
    2. Huiling Wu, 2016. "Optimal Investment-Consumption Strategy under Inflation in a Markovian Regime-Switching Market," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-17, July.
    3. He, Yong & Zhou, Xia & Chen, Peimin & Wang, Xiaoyang, 2022. "An analytical solution for the robust investment-reinsurance strategy with general utilities," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).

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