Pairwise counter-monotonicity

Paper: arXiv 2302.11701

Authors: Jean-Gabriel Lauzier, Liyuan Lin, Ruodu Wang

Abstract

We systematically study pairwise counter-monotonicity, an extremal notion of negative dependence. A stochastic representation and an invariance property are established for this dependence structure. We show that pairwise counter-monotonicity implies negative association, and it is equivalent to joint mix dependence if both are possible for the same marginal distributions. We find an intimate connection between pairwise counter-monotonicity and risk sharing problems for quantile agents. This result highlights the importance of this extremal negative dependence structure in optimal allocations for agents who are not risk averse in the classic sense.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a dense theoretical analysis of pairwise counter-monotonicity and its connection to risk sharing for quantile agents. It is mathematically sophisticated and highly novel in its theoretical findings, but it is entirely conceptual without empirical backtesting or real-world data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Systematic study of pairwise counter-monotonicity (PCM)"] --> B["Inputs: Marginal distributions & Quantile agents' risk preferences"]
    B --> C["Methodology: Theoretical formulation & Stochastic representation"]
    C --> D["Analysis: Relate PCM to Negative Association & Joint Mix Dependence"]
    D --> E["Application: Model risk sharing problems for non-classic risk-averse agents"]
    E --> F["Key Findings: PCM implies NA, equals Joint Mixability, & optimizes quantile risk sharing"]