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Asymptotics of random contractions
Insurance: Mathematics and Economics
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 is an element of (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.
Random contractions, Random scaling, Conditional tail expectation, Elliptical distributions, Spherical distributions, Subexponential distributions, Max domain of attraction, Risk aggregation, Ruin probability
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