CONTINUOUS-TIME RECURSIVE UTILITY MAXIMIZATION

Abstract

We investigate the continuous-time recursive utility maximization problem in this thesis. First, we formulate the continuous-time homothetic recursive utility, which is the continuous-time version of the Kreps-Porteus recursive utility. The infinite/finite time horizon recursive utility is characterized as the solution to an infinite/finite time horizon backward stochastic differential equation (BSDE). We establish the existence, uniqueness, comparison theorem, monotonicity, and concavity of the solution to the BSDE. Second, we solve the recursive utility maximization problem in a two-asset market under three cases: constant market parameters, observable regime switching parameters, and unobservable regime switching parameters. The verification theorem is proved and the optimal solution is obtained by solving the Hamilton-Jacobi-Bellman (HJB) equation for all the three cases. We also investigate the behaviors of the optimal solution with respect to the changes of market parameters by numerical method.