Paper: arXiv 2403.20171

Authors: Yuyu Chen, Paul Embrechts, Ruodu Wang

Abstract

We study the optimal decisions and equilibria of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are super-Pareto distributions, which include the class of extremely heavy-tailed Pareto distributions. Using a recent result on stochastic dominance, we show that for a portfolio of super-Pareto losses, non-diversification is preferred by decision makers equipped with well-defined and monotone risk measures. The phenomenon that diversification is not beneficial in the presence of super-Pareto losses is further illustrated by an equilibrium analysis in a risk exchange market. First, agents with super-Pareto losses will not share risks in a market equilibrium. Second, transferring losses from agents bearing super-Pareto losses to external parties without any losses may arrive at an equilibrium which benefits every party involved.

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 presents a strong, rigorous theoretical contribution to risk management and market equilibrium under extreme heavy-tailed (infinite-mean) distributions using stochastic dominance. However, it is entirely theoretical with no empirical data or backtesting, which limits its practical applicability without further real-world validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate optimal risk allocation & market equilibria for infinite-mean super-Pareto losses] --> B[Inputs: Super-Pareto loss distributions & monotone risk measures]
    B --> C[Methodology: Apply stochastic dominance results for extremely heavy-tailed risks]
    C --> D[Analysis 1: Individual Portfolio Optimization]
    C --> E[Analysis 2: Risk Exchange Market Equilibrium Model]
    D --> F[Finding 1: Non-diversification is optimal for individual decision makers]
    E --> G[Finding 2: Agents will not share risks internally, but external transfer can benefit all parties]