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).
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call