Life-cycle planning model with stochastic volatility and recursive preferences

Abstract

This study examines the optimal investment, consumption, and life insurance choices faced by a wage earner with recursive preferences within a finite time horizon. We posit that the financial market comprises a risk-free asset and a risky asset that follows a general stochastic volatility model. The objective of the wage earner is to identify optimal investment, consumption, and life insurance strategies that maximize the expected utility of discounted intertemporal consumption, legacy wealth, and terminal wealth throughout the uncertain lifespan. Using the dynamic programming principle, we derive the Hamilton-Jacobi-Bellman (HJB) equation to describe the optimal investment–consumption–insurance strategy and its corresponding value function. By solving the HJB equations, we derive the analytical solutions for the optimal strategy and value function in the cases of the exponential-polynomial form and the Heston's stochastic volatility model. Through numerical simulations, we investigate the impact of several parameters, providing further economic insights obtained in this study.