Paper: arXiv 2510.21650

Authors: Erhan Bayraktar, Bingyan Han, Jingjie Zhang

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs advanced mathematical tools like stochastic Perron’s method, viscosity solutions, and quasi-variational inequalities, representing high theoretical complexity. While it includes numerical results, there is no mention of backtesting, real market data, or implementation details, placing it firmly in the theoretical domain.

Research Flowchart

  flowchart TD
  A["Research Goal<br/>Goal-based portfolio selection<br/>with fixed transaction costs"] --> B["Methodology<br/>Stochastic Perron's Method"]
  B --> C["Formulation<br/>System of Quasi-Variational Inequalities"]
  C --> D["Analysis<br/>Viscosity Solution Theory"]
  D --> E{"Key Findings"}
  E --> F["Existence of optimal strategy<br/>& goal funding scheme"]
  E --> G["Complex trading regions<br/>& non-V-shaped strategy"]
  E --> H["Value function is unique<br/>viscosity solution"]