Paper: arXiv 2403.01468

Authors: Yuliya Mishura, Kostiantyn Ralchenko, Petro Zelenko, Volodymyr Zubchenko

Abstract

Entropic Value-at-Risk (EVaR) measure is a convenient coherent risk measure. Due to certain difficulties in finding its analytical representation, it was previously calculated explicitly only for the normal distribution. We succeeded to overcome these difficulties and to calculate Entropic Value-at-Risk (EVaR) measure for Poisson, compound Poisson, Gamma, Laplace, exponential, chi-squared, inverse Gaussian distribution and normal inverse Gaussian distribution with the help of Lambert function that is a special function, generally speaking, with two branches.

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 makes a valuable theoretical contribution by deriving closed-form expressions for Entropic Value-at-Risk (EVaR) across various heavy-tailed and common financial distributions using the Lambert W function. However, it is purely mathematical and lacks empirical validation, backtesting, or real-world market application.

Research Flowchart

  flowchart TD
    A[Research Goal: Derive analytical EVaR for non-Normal distributions] --> B[Input: Selected Probability Distributions]
    B --> C[Probability Distributions: Poisson, Gamma, Laplace, Exponential, Chi-sq, Inverse Gaussian, NIG]
    C --> D[Methodology: Apply Moment-Generating Functions & Chernoff Bound]
    D --> E[Computational Process: Solve optimization using multi-branch Lambert W function]
    E --> F[Outcomes: Closed-form EVaR expressions for all 8 target distributions]

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0 of 26 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.