Paper: arXiv 2212.14188

Authors: Ying Hu, Xiaomin Shi, Zuo Quan Xu

Abstract

This paper studies the monotone mean-variance (MMV) problem and the classical mean-variance (MV) problem with convex cone trading constraints in a market with random coefficients. We provide semiclosed optimal strategies and optimal values for both problems via certain backward stochastic differential equations (BSDEs). After noting the links between these BSDEs, we find that the two problems share the same optimal portfolio and optimal value. This generalizes the result of Shen and Zou $[$ SIAM J. Financial Math., 13 (2022), pp. SC99-SC112$]$ from deterministic coefficients to random ones.

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 advanced theoretical work utilizing backward stochastic differential equations (BSDEs) to address monotone mean-variance portfolio selection with random coefficients and convex constraints. While mathematically rigorous and novel in extending prior deterministic models, it is purely theoretical and completely lacks empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve MMV & MV problems<br/>with random coefficients & cone constraints] --> B[Inputs: Financial Market Model<br/>Multi-asset, random coefficients, convex cone]
    B --> C[Methodology: Formulate & Analyze<br/>System of BSDEs]
    C --> D[Compute Optimal Strategies<br/>& Value Functions via BSDE Solutions]
    D --> E[Compare MMV and MV<br/>Theoretical Outcomes]
    E --> F[Key Outcome: MMV & MV share<br/>identical optimal portfolio & value]
    F --> G[Finding: Generalizes Shen & Zou 2022<br/>from deterministic to random coefficients]