Explicit solutions of optimal consumption, investment and insurance problems with regime switching

Bin Zou and Abel Cadenillas

Insurance: Mathematics and Economics, 2014, vol. 58, issue C, 159-167

Abstract: We consider an investor who wants to select his optimal consumption, investment and insurance policies. Motivated by new insurance products, we allow not only the financial market but also the insurable loss to depend on the regime of the economy. The objective of the investor is to maximize his expected total discounted utility of consumption over an infinite time horizon. For the case of hyperbolic absolute risk aversion (HARA) utility functions, we obtain the first explicit solutions for simultaneous optimal consumption, investment, and insurance problems when there is regime switching. We determine that the optimal insurance contract is either no-insurance or deductible insurance, and calculate when it is optimal to buy insurance. The optimal policy depends strongly on the regime of the economy. Through an economic analysis, we calculate the advantage of buying insurance.

Keywords: Economic analysis; Hamilton–Jacobi–Bellman equation; Insurance; Regime switching; Utility maximization (search for similar items in EconPapers)
JEL-codes: C61 E32 E44 G11 G22 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:58:y:2014:i:c:p:159-167

DOI: 10.1016/j.insmatheco.2014.07.006

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