Optimal Life Insurance Purchase, Consumption and Investment on a financial market with multi-dimensional diffusive terms
AbstractWe 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1102.2263.
Date of creation: Feb 2011
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Web page: http://arxiv.org/
Other versions of this item:
- 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.
- NEP-ALL-2011-02-19 (All new papers)
- NEP-CIS-2011-02-19 (Confederation of Independent States)
- NEP-IAS-2011-02-19 (Insurance Economics)
- NEP-UPT-2011-02-19 (Utility Models & Prospect Theory)
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- 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.
- R. C. Merton, 1970.
"Optimum Consumption and Portfolio Rules in a Continuous-time Model,"
58, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- 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 247-57, August.
- 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.
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