Optimal life insurance purchase, consumption and investment on a financial market with multi-dimensional diffusive terms

I. Duarte, Diogo Pinheiro, Alberto Pinto and S. R. Pliska
Additional contact information
I. Duarte: Centro de Matematica da Universidade do Minho, Braga, Portugal
Alberto Pinto: Department of Mathematics, Faculty of Science, University of Porto
S. R. Pliska: Department of Finance, University of Illinois at Chicago, Chicago, IL 60607, USA

No 1102, CEMAPRE Working Papers from Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon

Abstract: We introduce an extension to Merton's famous continuous time model of optimal consumption and investment, in the spirit of previous works by Pliska and Ye, to allow for a wage earner to have a random lifetime and to use a portion of the income to purchase life insurance in order to provide for his estate, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities driven by multi-dimensional Brownian motion. We then provide a detailed analysis of the optimal consumption, investment, and insurance purchase strategies for the wage earner whose goal is to maximize the expected utility obtained from his family consumption, from the size of the estate in the event of premature death, and from the size of the estate at the time of retirement. We use dynamic programming methods to obtain explicit solutions for the case of discounted constant relative risk aversion utility functions and describe new analytical results which are presented together with the corresponding economic interpretations.

Pages: 20 pages
Date: 2011-10
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Citations: View citations in EconPapers (3)

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Working Paper: Optimal Life Insurance Purchase, Consumption and Investment on a financial market with multi-dimensional diffusive terms (2011)
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