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

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Listed:
  • I. Duarte

    (Centro de Matematica da Universidade do Minho, Braga, Portugal)

  • Diogo Pinheiro

    (CEMAPRE, School of Economics and Management (ISEG), Technical University of Lisbon)

  • Alberto A. 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)

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.

Suggested Citation

  • I. Duarte & Diogo Pinheiro & Alberto A. Pinto & S. R. Pliska, 2011. "Optimal life insurance purchase, consumption and investment on a financial market with multi-dimensional diffusive terms," CEMAPRE Working Papers 1102, Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon.
  • Handle: RePEc:cma:wpaper:1102
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    References listed on IDEAS

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    1. 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.
    2. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Jeanblanc, Monique & Martellini, Lionel, 2008. "Optimal investment decisions when time-horizon is uncertain," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1100-1113, December.
    3. Pliska, Stanley R. & Ye, Jinchun, 2007. "Optimal life insurance purchase and consumption/investment under uncertain lifetime," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1307-1319, May.
    4. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
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    Cited by:

    1. Pirvu, Traian A. & Zhang, Huayue, 2012. "Optimal investment, consumption and life insurance under mean-reverting returns: The complete market solution," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 303-309.

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