Pandemic-type Failures in Multivariate Brownian Risk Models

TL;DR

This paper investigates the probability of multiple simultaneous failures in multivariate Brownian risk models, providing bounds and asymptotic approximations relevant for pandemic-related risk analysis in finance and insurance.

Contribution

It introduces new bounds and asymptotic formulas for the probability of multiple failures in multivariate Brownian risk models, extending previous research.

Findings

Derived sharp bounds for failure probabilities

Provided asymptotic approximations for large time horizons

Extended existing results to more general settings

Abstract

Modelling of multiple simultaneous failures in insurance, finance and other areas of applied probability is important especially from the point of view of pandemic-type events. A benchmark limiting model for the analysis of multiple failures is the classical $d$-dimensional Brownian risk model (Brm), see [1]. From both theoretical and practical point of view, of interest is the calculation of the probability of multiple simultaneous failures in a given time horizon. The main findings of this contribution concern the approximation of the probability that at least $k$ out of $d$ components of Brm fail simultaneously. We derive both sharp bounds and asymptotic approximations of the probability of interest for the finite and the infinite time horizon. Our results extend previous findings of [2,3].