Optimal life-insurance selection and purchase within a market of several life-insurance providers |
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| Institution: | 1. Department of Mathematics, Faculty of Science, Birzeit University, Palestine;2. Department of Mathematics, Brooklyn College of the City University of New York, NY, USA;3. LIAAD — INESC TEC and Department of Mathematics, Faculty of Science, University of Porto, Portugal;1. Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE, School of Statistics, East China Normal University, Shanghai 200062, China;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada;1. School of Risk Management, Insurance, and Actuarial Science, St. John’s University, United States;2. Insurance/Risk Management & Business Economics/Policy, University of Pennsylvania - The Wharton School, United States;1. Coöperatie Dela, P.O. Box 522, 5600 AM Eindhoven, The Netherlands;2. CentER and Netspar, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands |
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| Abstract: | We consider the problem faced by a wage-earner with an uncertain lifetime having to reach decisions concerning consumption and life-insurance purchase, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities whose prices are determined by diffusive linear stochastic differential equations. We assume that life-insurance is continuously available for the wage-earner to buy from a market composed of a fixed number of life-insurance companies offering pairwise distinct life-insurance contracts. We characterize the optimal consumption, investment and life-insurance selection and purchase strategies for the wage-earner with an uncertain lifetime and 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 techniques to obtain an explicit solution in the case of discounted constant relative risk aversion (CRRA) utility functions. |
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| Keywords: | Uncertain lifetime Optimal consumption–investment Life-insurance purchase and selection Stochastic optimal control Dynamic programming |
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