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Mathematics Colloquium: Optimal Life Insurance Purchase, Consumption, and Portfolio under an Uncertain Life
4:10 p.m. Cleveland 247
Abstract: A continuous-time model is developed for determining a wage earner's optimal strategies for dividing lifetime income between the purchase of life insurance, consumption, and risky investment. The wage earner, whose lifetime is uncertain, seeks to maximize the expectation of (1) the utility of consumption while still alive and working, (2) the utility of the bequest upon premature death, and (3) the utility of the size of the estate upon retirement (if he or she lives that long). This talk will focus on how to analyze the proposed model by a dynamic programming approach and a martingale approach and how to numerically solve chain approximation approach. Numerical examples will be presented in an effort to explore economic implications.