Paper: arXiv 2605.02666

Authors: Jing He, Shuzhen Yang

Abstract

In this paper, we investigate a portfolio investment problem under volatility uncertainty and short-sale constraints market via sublinear expectation which is used to model volatility uncertainty. We assume the stocks admit volatility uncertainty. Thus the related portfolio has upper variance (maximum risk) and lower variance (minimum risk). By introducing a risk factor $w$ to conduct coupled modeling of the maximum and minimum risks, a simplified Sublinear Expectation Mean-Uncertainty Variance (SLE-MUV) model is constructed. Theoretically, we show that the Pareto frontier of the SLE-MUV model is a continuous convex curve, and its optimal solution can be expressed as a polynomial analytical expression with respect to the risk factor $w$. Empirically, we systematically test the practical performance of the SLE-MUV model and conduct comparative analysis with the traditional Mean-Variance (MV) model as the benchmark based on three sets of samples – simulated generated data, data of the US stock market and the A-share market. The empirical results show that the SLE-MUV model can significantly improving the risk-adjusted return of the investment portfolio.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10 (capped from 7.5: transaction costs not modelled; no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework using sublinear expectation to model volatility uncertainty alongside short-sale constraints, deriving an analytical polynomial Pareto frontier. It validates these theoretical contributions with comprehensive empirical testing across both simulated datasets and real market data (US and A-share markets), demonstrating significant performance improvements over classic Mean-Variance models.

Research Flowchart

  flowchart TD
    A[Research Goal: Portfolio Selection under Volatility Uncertainty & Short-Sale Constraints] --> B[Methodology: Sublinear Expectation Theory]
    B --> C[Model Construction: SLE-MUV Model via Risk Factor w]
    D[Inputs: Simulated, US Stock Market & A-share Market Data] --> E[Computational Analysis: Derive Analytical Solution & Optimise]
    C --> E
    E --> F[Theoretical Outcome: Continuous Convex Pareto Frontier]
    E --> G[Empirical Outcome: Outperforms MV Model in Risk-Adjusted Returns]

Cited References (32)

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  2. Conditional Value-at-Risk Under Reward-Penalty Mechanism with Applications to Robust Portfolio Management — → 2610.09246
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  6. Multi-objective Optimization Theory and Continuation Methods (2015)
  7. Improving Value-at-Risk prediction under model uncertainty (2020)
  8. Numerical methods for two-dimensional G -heat equation — → 2503.02395
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3 of 32 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.