Existence of Optimal Contracts for Principal-Agent Problem with Drift Control and Quadratic Effort Cost

Paper: arXiv 2503.08503

Authors: Xinfu Chen, Shuaijie Qian, Guan Qiao

Abstract

The existence of optimal contracts of the principal-agent problem is a long-standing problem. According to the general framework in Cvitanić et al. [2], this existence can be derived from the existence of a classical solution to a degenerated fully nonlinear parabolic partial differential equation problem. In this work we consider the simple case with drift control and quadratic cost function, then prove the existence of classical solution to that PDE.

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This is a purely theoretical mathematical finance paper that solves a long-standing open PDE regularity problem in continuous-time principal-agent theory (Cvitanić et al., 2018). While it features rigorous proofs and advanced stochastic control mathematics, it contains zero empirical data, backtesting, or code implementations.

Research Flowchart

  flowchart TD
    A[Research Goal: Prove Existence of Optimal Contracts in Principal-Agent Problem] --> B[Model Formulation: Drift Control with Quadratic Effort Cost]
    B --> C[Framework Application: Map Problem to Degenerate Nonlinear Parabolic PDE]
    C --> D[Mathematical Analysis: Prove Existence of Classical Solution to the PDE]
    D --> E[Outcome: Guaranteed Existence of Optimal Contracts & Characterization]