Here, there and everywhere: state-dependent time-inconsistent stochastic control

Paper: arXiv 2603.22022

Authors: Dylan Possamaï, Mateo Rodriguez Polo

Abstract

This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic differential equations (BSDEs). These equations encapsulate the equilibrium value function essential for resolving cases where the present state affecting the target functional triggers the inconsistency. Additionally, the paper offers an application exemplifying this theory through the time-inconsistent linear–quadratic regulator.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly advanced theoretical contribution to continuous-time stochastic control theory using systems of BSDEs. While mathematically rigorous and novel in its probabilistic representation, it is a purely theoretical paper with no empirical data or backtesting.

Research Flowchart

  flowchart TD
    A["Research Goal: Solve state-dependent<br>time-inconsistent stochastic control"] --> B["Input: Continuous-time system &<br>state-dependent target functional"]
    B --> C["Methodology: Develop equilibrium<br>value function framework"]
    C --> D["Derive system of Backward Stochastic<br>Differential Equations (BSDEs)"]
    D --> E["Application: Apply theory to<br>Time-Inconsistent Linear-Quadratic Regulator"]
    E --> F["Outcomes: Probabilistic representation<br>& exact equilibrium control strategies"]