Epstein-Zin Utility Maximization over Random Horizon
This talk focuses on solving the consumption-investment problem for an agent with stochastic differential utility of Epstein-Zin type. In contrast to prior literature, our time horizon is random, taken from the class of stopping times in the augmented Brownian filtration. Parameter specification is empirically relevant, with both relative risk-aversion and the elasticity of intertemporal substitution (EIS) in excess of one. The theory of BSDE (backward stochastic differential equations) is used to establish existence and uniqueness of the continuation value process, while martingale method is employed to derive optimal strategies. Relevant examples in decision theory will be discussed.