A new characterization of second-order stochastic dominance

Paper: arXiv 2402.13355

Authors: Yuanying Guan, Muqiao Huang, Ruodu Wang

Abstract

We provide a new characterization of second-order stochastic dominance, also known as increasing concave order. The result has an intuitive interpretation that adding a risk with negative expected value in adverse scenarios makes the resulting position generally less desirable for risk-averse agents. A similar characterization is also found for convex order and increasing convex order. The proof techniques for the main result are based on properties of Expected Shortfall, a family of risk measures that is popular in banking and insurance regulation. Applications in risk management and insurance are discussed.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical characterization of second-order stochastic dominance using Expected Shortfall properties and formal mathematical proofs. However, it is purely theoretical with minimal empirical data or backtesting, resulting in a high math, low empirical rigor profile.

Research Flowchart

  flowchart TD
    A[Research Goal: New Characterization of Second-Order Stochastic Dominance] --> B[Input: Expected Shortfall Risk Measures & SSD Properties]
    B --> C[Methodology: Analyze Negative Expected Values in Adverse Scenarios]
    C --> D[Mathematical Proofs: Apply Convex & Increasing Convex Orders]
    D --> E[Outcome: Characterization of SSD via Scenario-Based Risk]
    D --> F[Outcome: Applications in Insurance & Risk Management]