Tail Probabilities of Randomly Weighted Sums of Random Variables with Dominated Variation

Dingcheng Wang · Qihe Tang

98 citations0/0 files storedStochastic Models

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Probability and Risk Models Probability and Statistical Research Stochastic processes and financial applications

Abstract

This paper investigates the asymptotic behavior of tail probabilities of randomly weighted sums of independent heavy-tailed random variables, where the weights form another sequence of nonnegative and arbitrarily dependent random variables. The results obtained are further applied to derive asymptotic estimates for the ruin probabilities in a discrete time risk model with dependent stochastic returns.

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References

1997Modelling Extremal Events 1994Modelling of extremal events in insurance and finance 1994Subexponentiality of the product of independent random variables 2003Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks 2004Finite- and infinite-time ruin probabilities in the presence of stochastic returns on investments 2003Randomly Weighted Sums of Subexponential Random Variables with Application to Ruin Theory 2001Finite and infinite time ruin probabilities in a stochastic economic environment 1999On the ruin probabilities in a general economic environment

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2012Tail behavior of the product of two dependent random variables with applications to risk theory 2006Tail asymptotics for the sum of two heavy-tailed dependent risks 2010Approximation of the tail probability of randomly weighted sums of dependent random variables with dominated variation 2013On pairwise quasi-asymptotically independent random variables and their applications 2008Tail probabilities for infinite series of regularly varying random vectors

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