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On Merton’s Problem for Life Insurers

Published online by Cambridge University Press:  17 April 2015

Mogens Steffensen
Mogens Steffensen*
Affiliation:
Laboratory of Actuarial Mathematics, Institute of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark, e-mail: mogens@math.ku.dk
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Abstract

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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.

Keywords

Markov chainDividends and bonusPower utilityBellman equationDurable goods
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 34 , Issue 1 , May 2004 , pp. 5 - 25
Copyright
Copyright © ASTIN Bulletin 2004

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