Ruin probabilities for risk processes in a bipartite network. Issue 4 (1st October 2020)

• Record Type: Journal Article
• Authors: Behme, Anita; Klüppelberg, Claudia; Reinert, Gesine
• Is Part Of: Stochastic models. Volume 36:Issue 4(2020)
• Page Start: 548
• Page End: 573
• Publication Date: 2020-10-01
• Subjects: Bipartite network -- Cramér–Lundberg model -- exponential claim size distribution -- hitting probability -- multivariate compound Poisson process -- ruin theory -- Poisson approximation -- Pollaczek–Khintchine formula -- risk balancing network; primary: 60G51 -- 91B30 -- secondary: 94C15; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/15326349.2020.1760109
• Languages: English
• ISSNs: 1532-6349

Abstract

Abstract: This article studies risk balancing features in an insurance market by evaluating ruin probabilities for single and multiple components of a multivariate compound Poisson risk process. The dependence of the components of the process is induced by a random bipartite network. In analogy with the non-network scenario, a network ruin parameter is introduced. This random parameter, which depends on the bipartite network, is crucial for the ruin probabilities. Under certain conditions on the network and for light-tailed claim size distributions we obtain Lundberg bounds and, for exponential claim size distributions, exact results for the ruin probabilities. For large sparse networks, the network ruin parameter is approximated by a function of independent Poisson variables.