Goal-based portfolio choice model with discounted preference

This paper proposes goal-based portfolio selection model with discounted preference. Firstly, we discuss the goal-based portfolio selection problem and then modify the portfolio selection model based on cumulative prospect theory (CPT) as well as considering investors' discounted preference in psychology. Furthermore, our proposed model is solved by martingale methods and an analytical solution with satisfying behavior is derived. Finally, we select six different discounting functions to capture investors' strategic changes. Numerical results show that investor with future bias performs adequate confidence and patience whereas investor with present bias tends to the immediate interests.