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Optimal portfolio and insurance strategy with biometric risks, habit formation and smooth ambiguity

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  • Wang, Tao
  • Chen, Zhiping

Abstract

This paper studies the optimal consumption, investment, health insurance and life insurance strategy for a wage earner with smooth ambiguity, habit formation and biometric risks. The individual can invest in the financial market composed of a risk-free asset and a risky asset whose unknown market price results in ambiguity. The habit formation depends on historical consumption and satisfies an ordinary differential equation. Moreover, the biometric risks, which consist of health shock risk and mortality risk, can impact the individual's income and health state. The individual can purchase health insurance and life insurance to respectively deal with health shock risk and mortality risk, and aims at maximizing the total expected utility of consumption, legacy and terminal wealth. Using the dynamic programming technique, we derive the corresponding Hamilton-Jacobi-Bellman equation in the states of health and critical illness respectively, prove the verification theorem and obtain closed-form solutions for the optimal strategies. Finally, numerical experiments are carried out to illustrate the impact of risk aversion, ambiguity aversion, health shock and habit formation on the optimal strategy. The results reveal that the wage earner with different utility functions and different health states will show different behaviors in consumption, investment and insurance purchase.

Suggested Citation

  • Wang, Tao & Chen, Zhiping, 2024. "Optimal portfolio and insurance strategy with biometric risks, habit formation and smooth ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 118(C), pages 195-222.
    • Handle: RePEc:eee:insuma:v:118:y:2024:i:c:p:195-222
    DOI: 10.1016/j.insmatheco.2024.07.002
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    1. Fabrice Collard & Sujoy Mukerji & Kevin Sheppard & Jean‐Marc Tallon, 2018. "Ambiguity and the historical equity premium," Quantitative Economics, Econometric Society, vol. 9(2), pages 945-993, July.
    2. Migon, Helio S. & Moura, Fernando A.S., 2005. "Hierarchical Bayesian collective risk model: an application to health insurance," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 119-135, April.
    3. Holger Kraft & Claus Munk & Sebastian Wagner, 2018. "Housing Habits and Their Implications for Life-Cycle Consumption and Investment [The evolution of homeownership rates in selected OECD countries: demographic and public policy influences]," Review of Finance, European Finance Association, vol. 22(5), pages 1737-1762.
    4. Liu, Guo & Jin, Zhuo & Li, Shuanming, 2021. "Household Lifetime Strategies under a Self-Contagious Market," European Journal of Operational Research, Elsevier, vol. 288(3), pages 935-952.
    5. Mousa, A.S. & Pinheiro, D. & Pinto, A.A., 2016. "Optimal life-insurance selection and purchase within a market of several life-insurance providers," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 133-141.
    6. Christelis, Dimitris & Georgarakos, Dimitris & Sanz-de-Galdeano, Anna, 2020. "The impact of health insurance on stockholding: A regression discontinuity approach," Journal of Health Economics, Elsevier, vol. 69(C).
    7. Taboga, Marco, 2005. "Portfolio selection with two-stage preferences," Finance Research Letters, Elsevier, vol. 2(3), pages 152-164, September.
    8. Arthur E. Attema & Han Bleichrodt & Olivier L'Haridon, 2018. "Ambiguity preferences for health," Health Economics, John Wiley & Sons, Ltd., vol. 27(11), pages 1699-1716, November.
    9. Zhang, Jinhui & Purcal, Sachi & Wei, Jiaqin, 2021. "Optimal life insurance and annuity demand under hyperbolic discounting when bequests are luxury goods," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 80-90.
    10. 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.
    11. M. Dolores Collado & Martin Browning, 2007. "Habits and heterogeneity in demands: a panel data analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(3), pages 625-640.
    12. Kraft, Holger & Steffensen, Mogens, 2008. "Optimal Consumption and Insurance: A Continuous-time Markov Chain Approach," ASTIN Bulletin, Cambridge University Press, vol. 38(1), pages 231-257, May.
    13. Wei, Jiaqin & Cheng, Xiang & Jin, Zhuo & Wang, Hao, 2020. "Optimal consumption–investment and life-insurance purchase strategy for couples with correlated lifetimes," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 244-256.
    14. Munk, Claus & Sørensen, Carsten, 2010. "Dynamic asset allocation with stochastic income and interest rates," Journal of Financial Economics, Elsevier, vol. 96(3), pages 433-462, June.
    15. Pierre Martinon & Pierre Picard & Anasuya Raj, 2018. "On the design of optimal health insurance contracts under ex post moral hazard," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 43(2), pages 137-185, September.
    16. Christoph Hambel & Holger Kraft & Lorenz S. Schendel & Mogens Steffensen, 2017. "Life Insurance Demand Under Health Shock Risk," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(4), pages 1171-1202, December.
    17. Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
    18. Christoph Hambel & Holger Kraft & Claus Munk, 2022. "Solving life-cycle problems with biometric risk by artificial insurance markets," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2022(4), pages 307-327, April.
    19. Ning Wang & Zhuo Jin & Tak Kuen Siu & Ming Qiu, 2021. "Household consumption-investment-insurance decisions with uncertain income and market ambiguity," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(10), pages 832-865, November.
    20. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    21. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    22. Balter, Anne G. & Mahayni, Antje & Schweizer, Nikolaus, 2021. "Time-consistency of optimal investment under smooth ambiguity," European Journal of Operational Research, Elsevier, vol. 293(2), pages 643-657.
    23. Sundaresan, Suresh M, 1989. "Intertemporally Dependent Preferences and the Volatility of Consumption and Wealth," The Review of Financial Studies, Society for Financial Studies, vol. 2(1), pages 73-89.
    24. Pascal J. Maenhout, 2004. "Robust Portfolio Rules and Asset Pricing," The Review of Financial Studies, Society for Financial Studies, vol. 17(4), pages 951-983.
    25. Peng Yang & Zhiping Chen & Xiangyu Cui, 2021. "Equilibrium reinsurance strategies for n insurers under a unified competition and cooperation framework," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(10), pages 969-997, November.
    26. Zhongda Li & Lu Liu & Jiayu Shi & Yubing Sui, 2021. "Health insurance, risk attitudes, and household financial behavior," Health Economics, John Wiley & Sons, Ltd., vol. 30(5), pages 1239-1246, May.
    27. Boyle, Phelim & Tan, Ken Seng & Wei, Pengyu & Zhuang, Sheng Chao, 2022. "Annuity and insurance choice under habit formation," Insurance: Mathematics and Economics, Elsevier, vol. 105(C), pages 211-237.
    28. Guambe, Calisto & Kufakunesu, Rodwell, 2015. "A note on optimal investment–consumption–insurance in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 30-36.
    29. Tomas Björk & Mariana Khapko & Agatha Murgoci, 2017. "On time-inconsistent stochastic control in continuous time," Finance and Stochastics, Springer, vol. 21(2), pages 331-360, April.
    30. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
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    More about this item

    Keywords

    Biometric risks; Smooth ambiguity; Habit formation; Health insurance; Hamilton-Jacobi-Bellman equation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private

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