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Optimal investment and consumption decision of a family with life insurance

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  • Kwak, Minsuk
  • Shin, Yong Hyun
  • Choi, U Jin
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    Abstract

    We study an optimal portfolio and consumption choice problem of a family that combines life insurance for parents who receive deterministic labor income until the fixed time T. We consider utility functions of parents and children separately and assume that parents have an uncertain lifetime. If parents die before time T, children have no labor income and they choose the optimal consumption and portfolio with remaining wealth and life insurance benefit. The object of the family is to maximize the weighted average of utility of parents and that of children. We obtain analytic solutions for the value function and the optimal policies, and then analyze how the changes of the weight of the parents' utility function and other factors affect the optimal policies.

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    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 48 (2011)
    Issue (Month): 2 (March)
    Pages: 176-188

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    Handle: RePEc:eee:insuma:v:48:y:2011:i:2:p:176-188

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    Web page: http://www.elsevier.com/locate/inca/505554

    Related research

    Keywords: IE13 IB11 Life insurance Optimal investment/consumption Labor income Utility maximization Martingale method;

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    References

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    1. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
    2. Fortune, Peter, 1973. "A Theory of Optimal Life Insurance: Development and Tests," Journal of Finance, American Finance Association, vol. 28(3), pages 587-600, June.
    3. 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.
    4. Hakansson, Nils H, 1969. "Optimal Investment and Consumption Strategies under Risk, an Uncertain Lifetime, and Insurance," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(3), pages 443-66, October.
    5. Campbell, Ritchie A, 1980. " The Demand for Life Insurance: An Application of the Economics of Uncertainty," Journal of Finance, American Finance Association, vol. 35(5), pages 1155-72, December.
    6. Moore, Kristen S. & Young, Virginia R., 2006. "Optimal insurance in a continuous-time model," Insurance: Mathematics and Economics, Elsevier, vol. 39(1), pages 47-68, August.
    7. Fischer, Stanley, 1973. "A Life Cycle Model of Life Insurance Purchases," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(1), pages 132-52, February.
    8. Nielsen, Peter Holm & Steffensen, Mogens, 2008. "Optimal investment and life insurance strategies under minimum and maximum constraints," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 15-28, August.
    9. Huaxiong Huang & Moshe A. Milevsky & Jin Wang, 2008. "Portfolio Choice and Life Insurance: The CRRA Case," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(4), pages 847-872.
    10. Richard, Scott F., 1975. "Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model," Journal of Financial Economics, Elsevier, vol. 2(2), pages 187-203, June.
    11. Gabriele Stabile, 2006. "Optimal Timing Of The Annuity Purchase: Combined Stochastic Control And Optimal Stopping Problem," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 151-170.
    12. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    13. Huang, Huaxiong & Milevsky, Moshe A., 2008. "Portfolio choice and mortality-contingent claims: The general HARA case," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2444-2452, November.
    14. Lewis, Frank D, 1989. "Dependents and the Demand for Life Insurance," American Economic Review, American Economic Association, vol. 79(3), pages 452-67, June.
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    Cited by:
    1. Erhan Bayraktar & Virginia R. Young, 2012. "Life Insurance Purchasing to Maximize Utility of Household Consumption," Papers 1205.5958, arXiv.org, revised Jun 2013.
    2. Schendel, Lorenz S., 2014. "Consumption-investment problems with stochastic mortality risk," SAFE Working Paper Series 43, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.

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