A robust stochastic control problem with applications to monotone mean-variance problems

Paper: arXiv 2408.08595

Authors: Yuyang Chen, Tianjiao Hua, Peng Luo

Abstract

This paper studies a robust stochastic control problem with a monotone mean-variance cost functional and random coefficients. The main technique is to find the saddle point through two backward stochastic differential equations (BSDEs) with unbounded coefficients. We further show that the robust stochastic control problem shares the same optimal control and optimal value with the stochastic control problem with a mean-variance cost functional. The results obtained are then applied to monotone mean-variance and mean-variance portfolio selection problems and monotone mean-variance and mean-variance investment-reinsurance problems.

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 provides a rigorous theoretical contribution to continuous-time stochastic control and monotone mean-variance portfolio selection using BMO martingale techniques and BSDEs with unbounded coefficients. However, it is entirely mathematical and lacks empirical data, backtests, or computational implementations.

Research Flowchart

  flowchart TD
    A[Goal: Solve Robust Stochastic Control for Monotone Mean-Variance Problems] --> B[Inputs: Random Coefficients & Monotone Mean-Variance Functional]
    B --> C[Method: Formulate Saddle-Point Problem & System of 2 BSDEs]
    C --> D[Process: Solve BSDEs with Unbounded Coefficients]
    D --> E[Outcome: Prove Robust Problem Shares Optimal Control/Value with Standard Mean-Variance]
    E --> F[Applications: Portfolio Selection & Investment-Reinsurance Problems]