Paper: arXiv 2307.02178

Authors: Shuaijie Qian, Chen Yang

Abstract

This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs, in which the commonly used concavification principle for terminal value is no longer applicable. We establish a proper theoretical characterization of this problem via a two-step procedure. First, we examine the asymptotic terminal behavior of the value function, which implies that any transaction close to maturity only provides a marginal contribution to the utility. Second, we establish the theoretical foundation in terms of the discontinuous viscosity solution, incorporating the proper characterization of the terminal condition. Via extensive numerical analyses involving several types of utility functions, we find that the introduction of transaction costs into non-concave utility maximization problems can make it optimal for investors to hold on to a larger long position in the risky asset compared to the frictionless case, or hold on to a large short position in the risky asset despite a positive risk premium.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical treatment of portfolio selection with non-concave utility and transaction costs using discontinuous viscosity solutions. While mathematically deep and theoretical novel, it relies heavily on numerical analysis rather than empirical market data and backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Portfolio Selection with Non-Concave Utility & Transaction Costs] --> B[Input: Asset Dynamics, Transaction Costs & Non-Concave Utility Functions]
    B --> C[Step 1: Asymptotic Terminal Behavior Analysis]
    C --> D[Step 2: Discontinuous Viscosity Solution Characterization]
    D --> E[Numerical Analyses across Utility Types]
    E --> F[Findings: Transaction Costs Drive Larger Long Positions or Persistent Short Positions]