Goal-based portfolio selection with mental accounting

TL;DR

This paper develops a continuous-time portfolio model incorporating goal-based investment and mental accounting, revealing complex optimal strategies and interactions among multiple goals.

Contribution

It introduces a novel framework combining goal-based investment with mental costs and solves it using stochastic Perron's method, providing new insights into optimal rebalancing.

Findings

Free boundaries have complex shapes with bulges and notches.

Optimal strategies depend on wealth levels across portfolios.

Investors diversify among stocks and across different goals.

Abstract

We present a continuous-time portfolio selection framework that reflects goal-based investment principles and mental accounting behavior. In this framework, an investor with multiple investment goals constructs separate portfolios, each corresponding to a specific goal, with penalties imposed on fund transfers between these goals, referred to as mental costs. By applying the stochastic Perron's method, we demonstrate that the value function is the unique constrained viscosity solution of a Hamilton-Jacobi-Bellman equation system. Numerical analysis reveals several key features: the free boundaries exhibit complex shapes with bulges and notches; the optimal strategy for one portfolio depends on the wealth level of another; investors must diversify both among stocks and across portfolios; and they may postpone reallocating surplus from an important goal to a less important one until the former's deadline approaches.