Recursive Utility with Investment Gains and Losses: Existence, Uniqueness, and Convergence

We consider a generalization of the recursive utility model by adding a new component that represents utility of investment gains and losses, and study the utility process in this generalized model with constant elasticity of... [ view full abstract ]

We consider a generalization of the recursive utility model by adding a new component that represents utility of investment gains and losses, and study the utility process in this generalized model with constant elasticity of intertemporal substitution and relative risk aversion degree and with infinite time horizon. We prove that the utility process uniquely exists and is globally attracting when the agent derives nonnegative gain-loss utility and that it can be non-existent or non-unique otherwise. We then consider a portfolio selection problem with gain-loss utility and solve it by proving that the corresponding dynamic programming equation has a unique solution.