Ordering ruin probabilities for dependent claim streams.
type: Item
instance of: scholarly article
title: Ordering ruin probabilities for dependent claim streams.
zbMATH Open document ID: 1065.91034
DOI: 10.1016/S0167-6687(02)00206-8
author: Esther Frostig
published in: Insurance Mathematics \& Economics
publication date: 2003-11-16T00:00:00Z
review text: An insurer has \(s\) classes of customers/business in a set \(E=\{1,2,\dots,s\}\); when a shock of type \(K \subseteq E\) (following a Poisson process) occurs, claims in \(K\) arrive; ruin occurs if at some point of time a total claims net of premia exceed the insurer's reserves. The question addressed by the paper is whether ruin probability decreases if the \(s\) become less positively correlated. The complication is that since, any claim \(j \in E\) arrives whenever any shock \(K\) containing it occurs, to evaluate the degree of dependence of a vector of \(s\) individual claim processes, one has to consider the collection of the \(2^s\) types of shocks indexed by \(K\). It turns out that the appropriate dependence ordering is one that roughly says that a system of \(2^s\;K\)-type shocks is more independent than another if for any \(K\) and any partition of it the arrival rates of the elements of the partition are higher while that of \(K\) is lower. The corresponding vector of \(s\) classes is then less positively correlated, and the corresponding total-claim random variable is smaller in the stochastic convex order (roughly same mean smaller variance). This, by an existing result, implies that the ruin probability is lower for any level of initial capital.
reviewed by: Salvatore Modica
Mathematics Subject Classification ID: 91B30
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 2004072
zbMATH Keywords: supermodular vector orderings
zbMATH Keywords: ruin probabilities
zbMATH Keywords: Poisson processes
MaRDI profile type: Publication
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full work available at URL: s0167-6687(02)00206-8
OpenAlex ID: W2075175593
description: scientific article; zbMATH DE number 2004072