Paper: arXiv 2304.06859

Authors: Peter B. Lerner

Abstract

Copulas are widely used in financial economics as well as in other areas of applied mathematics. Yet, there is much arbitrariness in their choice. The author proposes “a natural copula” concept, which minimizes Wasserstein distance between distributions in some space, in which both these distributions are embedded. Transport properties and hydrodynamic interpretation are discussed with two examples of distributions of financial significance. A natural copula can be parsimoniously estimated by the methods of linear programming.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces a mathematically elegant and original theoretical framework using optimal transport and Wasserstein distance to define a ’natural copula’. However, it remains predominantly theoretical with limited empirical backtesting or real-world financial data validation provided in the abstract.

Research Flowchart

  flowchart TD
    A[Research Goal: Address Arbitrariness in Copula Selection] --> B[Embed Target Distributions into Shared Metric Space]
    C[Input: Multi-Asset Financial Distributions] --> D[Optimal Transport: Minimize Wasserstein Distance]
    B --> D
    D --> E[Computation: Estimate Parsimoniously via Linear Programming]
    E --> F[Outcomes: Establish Natural Copula & Hydrodynamic Properties]