Paper: arXiv 2306.08519

Authors: Jin Hyuk Choi, Jetlir Duraj, Kim Weston

Abstract

We prove the existence of a continuous-time Radner equilibrium with multiple agents and transaction costs. The agents are incentivized to trade towards a targeted number of shares throughout the trading period and seek to maximize their expected wealth minus a penalty for deviating from their targets. Their wealth is further reduced by transaction costs that are proportional to the number of stock shares traded. The agents’ targeted number of shares is publicly known, making the resulting equilibrium fully revealing. In equilibrium, each agent optimally chooses to trade for an initial time interval before stopping trade. Our equilibrium construction and analysis involves identifying the order in which the agents stop trade. The transaction cost level impacts the equilibrium stock price drift. We analyze the equilibrium outcomes and provide numerical examples.

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 continuous-time theoretical framework establishing a Radner equilibrium with multiple agents and transaction costs. While mathematically sophisticated and novel in its equilibrium construction, it lacks empirical backtesting and real-market data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Prove continuous-time Radner<br/>equilibrium with transaction costs & targeted trading] --> B[Inputs: Public agent share targets,<br/>proportional transaction costs, & wealth penalties]
    B --> C[Methodology: Formulate multi-agent continuous-time<br/>utility maximization framework]
    C --> D[Equilibrium Construction: Determine precise<br/>sequence & timing of agent trade stoppings]
    D --> E[Analysis & Numerical Simulations:<br/>Evaluate impact of transaction costs on price drift]
    E --> F[Key Findings: Equilibrium is fully revealing;<br/>agents trade initially then stop;<br/>costs directly alter stock price drift]