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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
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/abs/0801.0195
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Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0801.0195.

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Date of creation: Dec 2007
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Handle: RePEc:arx:papers:0801.0195

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  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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  6. 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. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
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