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Stochastic utilities with subsistence and satiation: Optimal life insurance purchase, consumption and investment

Jinchun Ye

Insurance: Mathematics and Economics, 2019, vol. 89, issue C, 193-212

Abstract: We introduce stochastic utilities such that utility of any fixed amount of interest is a stochastic process or random variable. Also, there exist stochastic (or random) subsistence and satiation levels associated with stochastic utilities. Then, we consider optimal consumption, life insurance purchase and investment strategies to maximize the expected utility of consumption, bequest and pension with respect to stochastic utilities. We use the martingale approach to solve the optimization problem in two steps. First, we solve the optimization problem with an equality constraint which requires that the present value of consumption, bequest and pension is equal to the present value of initial wealth and income stream. Second, if the optimization problem is feasible, we obtain the explicit representations of the replicating life insurance purchase and portfolio strategies. As an application of our general results, we consider a family of stochastic utilities which have hyperbolic absolute risk aversion (HARA).

Keywords: Stochastic utilities; Subsistence and satiation levels; Balance equation; Martingale method; Backward stochastic differential equations; Replicating life insurance purchase and portfolio strategies (search for similar items in EconPapers)
JEL-codes: C61 D11 D81 G11 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.insmatheco.2019.10.008

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