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An optimal life insurance policy in the investment-consumption problem in an incomplete market

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  • Masahiko Egami
  • Hideki Iwaki
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    Abstract

    This paper considers an optimal life insurance for a householder subject to mortality risk. The household receives a wage income continuously, which is terminated by unexpected (premature) loss of earning power or (planned and intended) retirement, whichever happens first. In order to hedge the risk of losing income stream by householder's unpredictable event, the household enters a life insurance contract by paying a premium to an insurance company. The household may also invest their wealth into a financial market. The problem is to determine an optimal insurance/investment/consumption strategy in order to maximize the expected total, discounted utility from consumption and terminal wealth. To reflect a real-life situation better, we consider an incomplete market where the householder cannot trade insurance contracts continuously. To our best knowledge, such a model is new in the insurance and finance literature. The case of exponential utilities is considered in detail to derive an explicit solution. We also provide numerical experiments for that particular case to illustrate our results.

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    File URL: http://arxiv.org/pdf/0801.0195
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0801.0195.

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    Date of creation: Dec 2007
    Date of revision: May 2011
    Handle: RePEc:arx:papers:0801.0195

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    Web page: http://arxiv.org/

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    1. Henderson, Vicky, 2005. "Explicit solutions to an optimal portfolio choice problem with stochastic income," Journal of Economic Dynamics and Control, Elsevier, vol. 29(7), pages 1237-1266, July.
    2. Marceau, Etienne & Gaillardetz, Patrice, 1999. "On life insurance reserves in a stochastic mortality and interest rates environment," Insurance: Mathematics and Economics, Elsevier, vol. 25(3), pages 261-280, December.
    3. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
    4. He, Hua & Pages, Henri F, 1993. "Labor Income, Borrowing Constraints, and Equilibrium Asset Prices," Economic Theory, Springer, vol. 3(4), pages 663-96, October.
    5. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    6. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
    7. Knut Aase & Svein-Arne Persson, 1996. "Valuation of the Minimum Guaranteed Return Embedded in Life Insurance Products," Center for Financial Institutions Working Papers 96-20, Wharton School Center for Financial Institutions, University of Pennsylvania.
    8. Cuoco, Domenico, 1997. "Optimal Consumption and Equilibrium Prices with Portfolio Constraints and Stochastic Income," Journal of Economic Theory, Elsevier, vol. 72(1), pages 33-73, January.
    9. Zvi Bodie & William Samuelson, 1989. "Labor Supply Flexibility and Portfolio Choice," NBER Working Papers 3043, National Bureau of Economic Research, Inc.
    10. Iwaki, Hideki & Kijima, Masaaki & Morimoto, Yuji, 2001. "An economic premium principle in a multiperiod economy," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 325-339, June.
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