Optimal contract design via relaxation: application to the problem of brokerage fee for a client with private signal

Paper: arXiv 2307.07010

Authors: Guillermo Alonso Alvarez, Sergey Nadtochiy

Abstract

In this paper we show how the relaxation techniques can be used to establish the existence of an optimal contract in presence of information asymmetry. The method we illustrate was initially motivated by the problem of designing optimal brokerage fees, but it does apply to other optimal contract problems, in which (i) the agent controls linearly the drift of a diffusion process, (ii) the direct dependence of the principal’s and the agent’s objectives on the strategy of the agent is of a special form, and (iii) the space of admissible contracts is compact. This method is then applied to establish existence of an optimal brokerage fee in a market model with a private trading signal observed by the broker’s client but not by the broker.

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 provides a rigorous, highly mathematical approach to principal-agent contract design using relaxation techniques for drift-controlled diffusion processes. However, it is purely theoretical with minimal to no empirical validation or real-world data backtesting.

Research Flowchart

  flowchart TD
    A[Research Goal: Find optimal contract under information asymmetry] --> B[Market Inputs: Broker-client model, Private trading signal, Compact contract space]
    B --> C[Methodology: Formulate Principal-Agent model via diffusion process]
    C --> D[Computational Step: Apply relaxation techniques to linear drift control]
    D --> E[Key Outcome: Proved existence of optimal brokerage fee structure]