Goal-based portfolio selection with mental accounting

2025-06-07

AI Summary

This paper addresses the challenge of modeling mental accounting behavior in goal-directed investing by proposing a continuous-time multi-account dynamic asset allocation framework: wealth is partitioned into separate accounts aligned with distinct financial goals, and inter-account fund transfers are explicitly penalized by psychological costs. Methodologically, it pioneers the integration of mental accounting into multi-objective dynamic optimization, formulating a coupled system of Hamilton–Jacobi–Bellman (HJB) equations, solved via the stochastic Perron method; uniqueness of the value function is established using constrained viscosity solution theory. Theoretically, it uncovers novel phenomena—including inter-account wealth dependence, non-monotonic free boundaries, and deadline-driven rebalancing delays. Numerical results demonstrate that the optimal strategy entails dual diversification across both stocks and accounts, with critical surplus reallocation deferred markedly toward the goal deadline; the free boundary exhibits a complex convex-concave structure.

Technology Category

• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

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.

Problem

• Modeling goal-based portfolio selection with mental accounting behavior
• Analyzing optimal strategies for multiple goal-dependent portfolios
• Exploring wealth interdependence and diversification across goal portfolios

Innovation

• Continuous-time portfolio selection with mental accounting
• Stochastic Perron's method for viscosity solutions
• Diversification across stocks and portfolios