Optimal investment, consumption and life insurance under mean-reverting returns: The complete market solution

This paper considers the problem of optimal investment, consumption and life insurance acquisition for a wage earner who has CRRA (constant relative risk aversion) preferences. The market model is complete, continuous, the uncertainty is driven by Brownian motion and the stock price has mean reverti...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2012-09, Vol.51 (2), p.303-309
Main Authors: Pirvu, Traian A., Zhang, Huayue
Format: Article
Language:English
Subjects:
Acquisitions
Consumption
Dynamic programming
Life insurance
Mean reverting drift
Portfolio allocation
Portfolio investments
Risk aversion
Stock prices
Studies
Uncertainty
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Summary:This paper considers the problem of optimal investment, consumption and life insurance acquisition for a wage earner who has CRRA (constant relative risk aversion) preferences. The market model is complete, continuous, the uncertainty is driven by Brownian motion and the stock price has mean reverting drift. The problem is solved by dynamic programming approach and the HJB equation is shown to have closed form solution. Numerical experiments explore the impact market price of risk has on the optimal strategies. ► We consider the problem of optimal investment, consumption and life insurance. ► We provide closed form solution by using dynamic programming. ► We perform numerical experiments.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2012.05.002