Optimal Investment and Consumption Strategies with General and Linear Transaction Costs under CRRA Utility

Paper: arXiv 2304.07672

Authors: Yingting Miao, Qiang Zhang

Abstract

Transaction costs play a critical role in asset allocation and consumption strategies in portfolio management. We apply the methods of dynamic programming and singular perturbation expansion to derive the closed-form leading solutions to this problem for small transaction costs with arbitrary transaction cost structure by maximizing the expected CRRA (constant relative risk aversion) utility function for this problem. We also discuss in detail the case which consists of both fixed and proportional transaction costs.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using stochastic dynamic programming and singular perturbation expansions to derive closed-form solutions under complex transaction cost structures. However, it lacks empirical backtesting and data validation, focusing almost entirely on mathematical derivation.

Research Flowchart

  flowchart TD
    A[Goal: Optimal Investment & Consumption<br>with Transaction Costs under CRRA Utility] --> B[Inputs: Multi-Asset Model &<br>Arbitrary Transaction Cost Structure]
    B --> C[Method: Apply Dynamic Programming<br>& Hamilton-Jacobi-Bellman Equations]
    C --> D[Method: Apply Singular Perturbation Expansion<br>for Small Costs]
    D --> E[Outcomes: Closed-form Leading Solutions<br>for Investment & Consumption]
    E --> F[Specific Case: Combined Fixed & Proportional<br>Transaction Costs Detailed]