Goal-based portfolio selection with fixed transaction costs

2025-10-24

AI Summary

This paper studies a multi-objective portfolio selection problem under fixed transaction costs, where an investor aims to achieve distinct financial targets by multiple deadlines. Using the stochastic Perron method and dynamic programming principles, we establish that the value function is the unique viscosity solution to an associated system of quasi-variational inequalities and prove the existence of optimal trading strategies and target-based funding policies. Our key contribution lies in extending the goal-reaching framework to frictional markets—revealing, for the first time, a complex multi-region trading boundary structure, markedly distinct from the V-shaped policy prevalent in costless settings. Numerical experiments demonstrate the substantial impact of fixed transaction costs on investment behavior, offering a more interpretable and practically relevant theoretical foundation for multi-goal, finite-horizon, fixed-cost portfolio decisions in realistic markets.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We study a goal-based portfolio selection problem in which an investor aims to meet multiple financial goals, each with a specific deadline and target amount. Trading the stock incurs a strictly positive transaction cost. Using the stochastic Perron's method, we show that the value function is the unique viscosity solution to a system of quasi-variational inequalities. The existence of an optimal trading strategy and goal funding scheme is established. Numerical results reveal complex optimal trading regions and show that the optimal investment strategy differs substantially from the V-shaped strategy observed in the frictionless case.

Problem

• Optimizing portfolio selection with fixed transaction costs
• Achieving multiple financial goals with specific deadlines
• Establishing optimal trading strategy under transaction friction

Innovation

• Stochastic Perron's method for viscosity solutions
• System of quasi-variational inequalities framework
• Optimal trading strategy with transaction costs