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Optimal investment and life insurance strategies under minimum and maximum constraints

  • Nielsen, Peter Holm
  • Steffensen, Mogens
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    We derive optimal strategies for an individual life insurance policyholder who can control the asset allocation as well as the sum insured (the amount to be paid out upon death) throughout the policy term. We first consider the problem in a pure form without constraints (except nonnegativity on the sum insured) and then in a more general form with minimum and/or maximum constraints on the sum insured. In both cases we also provide the optimal life insurance strategies in the case where risky-asset investments are not allowed (or not taken into consideration), as in basic life insurance mathematics. The optimal constrained strategies are somewhat more complex than the unconstrained ones, but the latter can serve to ease the understanding and implementation of the former.

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    File URL: http://www.sciencedirect.com/science/article/B6V8N-4PSK8NV-1/2/b1ad50c54e8384274f6d0c182edc1272
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    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 43 (2008)
    Issue (Month): 1 (August)
    Pages: 15-28

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    Handle: RePEc:eee:insuma:v:43:y:2008:i:1:p:15-28
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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    1. 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.
    2. Hong, Jay H. & Rios-Rull, Jose-Victor, 2007. "Social security, life insurance and annuities for families," Journal of Monetary Economics, Elsevier, vol. 54(1), pages 118-140, January.
    3. Erhan Bayraktar & Virginia R. Young, 2007. "Correspondence between Lifetime Minimum Wealth and Utility of Consumption," Papers math/0703820, arXiv.org.
    4. 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.
    5. 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.
    6. Cox, John C. & Huang, Chi-fu, 1991. "A variational problem arising in financial economics," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 465-487.
    7. 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.
    8. repec:cup:cbooks:9780521868778 is not listed on IDEAS
    9. 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.
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