Asymptotics of random contractions

By Enkelejd Hashorva, Anthony G. Pakes, Qihe Tang. 2010

89 citations recorded by the source corpus.

In this paper we discuss the asymptotic behaviour of random contractions X=RS, where R, with distribution function F, is a positive random variable independent of S[set membership, variant](0,1). Random contractions appear naturally in insurance and finance. Our principal contribution is the derivation of the tail asymptotics of X assuming that F is in the max-domain of attraction of an extreme value distribution and the distribution function of S satisfies a regular variation property. We apply our result to derive the asymptotics of the probability of ruin for a particular discrete-time risk model. Further we quantify in our asymptotic setting the effect of the random scaling on the Conditional Tail Expectations, risk aggregation, and derive the joint asymptotic distribution of linear combinations of random contractions.

Subfields: Demography, Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/341773336ec23fd4af94eb98d0c1ff57d5dafd2e

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Citations in the corpus

The Finite-Time Ruin Probability with Dependent Insurance and Financial Risks (2011, background): “1(i) of Jiang and Tang (2011) for a result more general than (4.”
Extremal dependence of random scale constructions (2018, methodology): “Hashorva (2010) details calculation of ηX assuming R to be in the Gumbel MDA, providing an alternative perspective on the derivation.”
Randomly weighted sums of subexponential random variables with application to capital allocation (2014, background): “Keywords Asymptotics · Capital allocation · Matuszewska indices · Randomly weighted sum · Subexponentiality AMS 2000 Subject Classifications Primary—62E20; Secondary—60G70”
Asymptotics for Risk Capital Allocations Based on Conditional Tail Expectation (2011, unknown): “For a distribution function F ∈ MDA(Λ), conditions on its auxiliary function a(·) under which F ∈ S are available in Goldie and Resnick (1988) and Hashorva et al. (2010).”