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An R-Based Landscape Validation of a Competing Risk Model

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Pandemic-type failures in multivariate Brownian risk models.

Krzysztof Dȩbicki¹, Enkelejd Hashorva², Nikolai Kriukov²

¹Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland.

Extremes

|February 28, 2022

Summary

This study provides new approximations for simultaneous failures in the d-dimensional Brownian risk model (Brm), crucial for pandemic-type events. We offer sharp bounds and asymptotic formulas for the probability of at least k component failures.

Keywords:

Exact asymptotics Failure time Multivariate Brownian risk model Pandemic-type events Probability of multiple simultaneous failures Simultaneous ruin probability

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Area of Science:

Applied Probability
Financial Mathematics
Risk Theory

Background:

Modelling multiple simultaneous failures is critical in insurance and finance, particularly for pandemic-like events.
The d-dimensional Brownian risk model (Brm) serves as a benchmark for analyzing such failures.

Purpose of the Study:

To approximate the probability of at least k simultaneous failures among d components in the Brm.
To derive sharp bounds and asymptotic approximations for this probability over finite and infinite time horizons.

Main Methods:

Development of analytical techniques for approximating ruin probabilities in a multi-dimensional setting.
Derivation of sharp lower and upper bounds for the probability of simultaneous component failures.
Asymptotic analysis for both finite and infinite time horizons.

Main Results:

Novel sharp bounds and asymptotic approximations for the probability of at least k simultaneous component failures in the Brm.
The derived results extend and improve upon existing findings in the field of ruin theory.
Accurate estimations for the likelihood of multiple system failures within specified timeframes.

Conclusions:

The study offers significant advancements in the theoretical and practical understanding of multiple failure events.
The findings are valuable for risk management in financial and insurance sectors facing systemic risks.
This research provides enhanced tools for quantifying the probability of complex failure scenarios.