Cash non-additive risk measures: horizon risk and generalized entropy

Paper: arXiv 2401.14443

Authors: Giulia Di Nunno, Emanuela Rosazza Gianin

Abstract

Horizon risk (see arXiv:2301.04971) is studied in the context of cash non-additive fully-dynamic risk measures induced by BSDEs. Furthermore, we introduce a risk measure based on generalized Tsallis entropy which can dynamically evaluate the riskiness of losses considering both horizon risk and interest rate uncertainty. The new q-entropic risk measure on losses can be used as a quantification of capital requirement.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using Backward Stochastic Differential Equations (BSDEs) and generalized Tsallis entropy to model cash non-additive dynamic risk measures and horizon risk. However, it is almost purely theoretical with minimal empirical backtesting or real-world data application, impacting its immediate reproducibility and empirical rigor.

Research Flowchart

  flowchart TD
    A[Goal: Quantify Risk under Horizon & Interest Rate Uncertainty] --> B[Input: Financial Loss Distributions & Dynamic Timelines]
    B --> C[Formulate Cash Non-Additive Fully-Dynamic BSDEs]
    C --> D[Incorporate Generalized Tsallis Entropy]
    D --> E[Compute Dynamic q-Entropic Risk Measure]
    E --> F[Outcome: Advanced Capital Requirement Framework]