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

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  • Zou, Bin
  • Cadenillas, Abel

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.

Suggested Citation

  • Zou, Bin & Cadenillas, Abel, 2014. "Explicit solutions of optimal consumption, investment and insurance problems with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 159-167.
    • Handle: RePEc:eee:insuma:v:58:y:2014:i:c:p:159-167
    DOI: 10.1016/j.insmatheco.2014.07.006
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    References listed on IDEAS

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    Cited by:

    1. Yanlin Shi & Lingbing Feng & Tong Fu, 2020. "Markov Regime-Switching in-Mean Model with Tempered Stable Distribution," Computational Economics, Springer;Society for Computational Economics, vol. 55(4), pages 1275-1299, April.
    2. Li, Wenyuan & Tan, Ken Seng & Wei, Pengyu, 2021. "Demand for non-life insurance under habit formation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 38-54.
    3. Bin Zou & Abel Cadenillas, 2017. "Optimal Investment and Liability Ratio Policies in a Multidimensional Regime Switching Model," Risks, MDPI, vol. 5(1), pages 1-22, January.
    4. Gaurav Khemka & Adam Butt, 2017. "Non-Parametric Integral Estimation Using Data Clustering in Stochastic dynamic Programming: An Introduction Using Lifetime Financial Modelling," Risks, MDPI, vol. 5(4), pages 1-17, October.
    5. Andreas Lichtenstern & Pavel V. Shevchenko & Rudi Zagst, 2019. "Optimal life-cycle consumption and investment decisions under age-dependent risk preferences," Papers 1908.09976, arXiv.org.

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    More about this item

    Keywords

    Economic analysis; Hamilton–Jacobi–Bellman equation; Insurance; Regime switching; Utility maximization;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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