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On Merton’s Problem for Life Insurers

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  • Steffensen, Mogens

Abstract

This paper deals with optimal investment and redistribution of the free reserves connected to life and pension insurance contracts in form of dividends and bonus. Formulated appropriately this problem can be viewed as a modification of Merton’s problem of optimal consumption and investment with a very particular form of consumption and utility hereof. Both are linked to a finite state Markov chain. We distinguish between utility optimization of dividends, where a semi-explicit result is obtained, and utility optimization of bonus payments. The latter connects to the financial notion of durable goods and allows for an explicit solution only in very special cases.

Suggested Citation

  • Steffensen, Mogens, 2004. "On Merton’s Problem for Life Insurers," ASTIN Bulletin, Cambridge University Press, vol. 34(1), pages 5-25, May.
    • Handle: RePEc:cup:astinb:v:34:y:2004:i:01:p:5-25_01
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    Cited by:

    1. Hong‐Chih Huang, 2010. "Optimal Multiperiod Asset Allocation: Matching Assets to Liabilities in a Discrete Model," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 451-472, June.
    2. Jarner, Søren Fiig & Kronborg, Morten Tolver, 2016. "Entrance times of random walks: With applications to pension fund modeling," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 1-20.
    3. Fahrenwaldt, Matthias A. & Sun, Chaofan, 2020. "Expected utility approximation and portfolio optimisation," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 301-314.

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