Asset-liability management with Epstein-Zin utility under stochastic interest rate and unknown market price of risk

This paper solves a consumption-investment choice problem with Epstein-Zin recursive utility under partial information--unobservable market price of risk. The main novelty is the introduction of a terminal liability constraint, a feature directly motivated by practical portfolio management and insurance applications but absent from the recursive utility literature. Such constraint gives rise to a coupled forward-backward stochastic differential equation (FBSDE) whose well-posedness has not been addressed in earlier work. We provide an explicit solution to this FBSDE system--contrasting with the typical existence and uniqueness results with no closed-form expressions in the literature. Under mild additional assumptions, we also establish the Malliavin differentiability of the solution allowing the optimal investment strategy to be expressed as a conditional expectation of random variables that can be efficiently simulated. These results allows us to obtain the explicit expressions of the optimal controls and the value function. Finally, we quantify the utility loss from ignoring learning about the market price of risk, highlighting the economic significance of partial information.