Insurance Applications of Some New Dependence Models derived from\n Multivariate Collective Models

2016/03/06 by Enkelejd Hashorva, Hashorva, Enkelejd, Gildas Ratovomirija +3
Computer Science · Decision Sciences · Mathematics · #60G15 #62F10 #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1603.01871

openalex publication_date 2016/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider two different portfolios which have claims triggered by the same\nevents. Their corresponding collective model over a fixed time period is given\nin terms of individual claim sizes (X_i,Y_i), i\≥ 1 and a claim counting\nrandom variable N. In this paper we are concerned with the joint distribution\nfunction F of the ecelargest claim sizes (X_N:N, Y_N:N). By allowing\nN to depend on some parameter, say \θ, then F=F(\θ) is for\nvarious choices of N a tractable parametric family of bivariate distribution\nfunctions. We present three applications of the implied parametric models to\nsome data from the literature and a new data set from a Swiss insurance\ncompany. Furthermore, we investigate both distributional and asymptotic\nproperties of (X_N:N, Y_N:N).\n

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