Unified Asymptotics For Investment Under Illiquidity: Transaction Costs And Search Frictions

Paper: arXiv 2407.13547

Authors: Tae Ung Gang, Jin Hyuk Choi

Abstract

This paper investigates the optimal investment problem in a market with two types of illiquidity: transaction costs and search frictions. Extending the framework established by arXiv:2101.09936, we analyze a power-utility maximization problem where an investor encounters proportional transaction costs and trades only when a Poisson process triggers trading opportunities. We show that the optimal trading strategy is described by a no-trade region. We introduce a novel asymptotic framework applicable when both transaction costs and search frictions are small. Using this framework, we derive explicit asymptotics for the no-trade region and the value function along a specific parametric curve. This approach unifies existing asymptotic results for models dealing exclusively with either transaction costs or search frictions.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework establishing unified asymptotics for portfolio optimization under both transaction costs and Poisson search frictions. While mathematically sophisticated and novel in its asymptotic scaling approach, it is entirely theoretical and lacks empirical backtesting or real-world data application.

Research Flowchart

  flowchart TD
    A[Research Goal: Unify Optimal Investment Asymptotics for Transaction Costs & Search Frictions] --> B[Model Setup: Power-Utility Maximization with Proportional Costs & Poisson Search Frictions]
    B --> C[Methodology: Extend Framework & Apply Novel Asymptotic Expansion for Small Frictions]
    C --> D[Computational Process: Solve Free-Boundary Problem for No-Trade Region & Value Function]
    D --> E[Key Finding 1: Explicit Asymptotics for Optimal No-Trade Region Boundaries]
    D --> F[Key Finding 2: Unified Parametric Formula Connecting Pure Transaction Cost & Search Friction Models]