Multivariate Subexponential Distributions and Their Applications

2015/09/17 by Gennady Samorodnitsky, Samorodnitsky, Gennady, Julian Sun +1 · 5 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Probability and Risk Models #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.1509.05353

Abstract

We propose a new definition of a multivariate subexponential distribution. We compare this definition with the two existing notions of multivariate subexponentiality, and compute the asymptotic behaviour of the ruin probability in the context of an insurance portfolio, when multivariate subexponentiality holds. Previously such results were available only in the case of multivariate regularly varying claims.

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• Multivariate subexponentiality and interplay of insurance and financial risks in a renwal risk model
• Infinite-time ruin probability of a multivariate renewal risk model with Brownian perturbations
• Asymptotics for aggregated interdependent multivariate subexponential claims with general investment returns
• The Bivariate regular variation of randomly weighted sums revisited in the presence of interdependence
• Uniform asymptotics for a multidimensional renewal risk model with multivariate subexponential claims

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