Frequency and Severity Dependence in the Collective Risk Model: An Approach Based on Sarmanov Distribution

Catalina Bolancé and Raluca Vernic
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Catalina Bolancé: Department of Econometrics, Riskcenter-IREA University of Barcelona, Av. Diagonal, 690, 08034 Barcelona, Spain
Raluca Vernic: Faculty of Mathematics and Computer Science, Ovidius University of Constanta, 124 Mamaia Blvd., Constanta, and Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Calea 13 Septembrie 13, 050711 Bucharest, Romania

Mathematics, 2020, vol. 8, issue 9, 1-17

Abstract: In actuarial mathematics, the claims of an insurance portfolio are often modeled using the collective risk model, which consists of a random number of claims of independent, identically distributed (i.i.d.) random variables (r.v.s) that represent cost per claim. To facilitate computations, there is a classical assumption of independence between the random number of such random variables (i.e., the claims frequency) and the random variables themselves (i.e., the claim severities). However, recent studies showed that, in practice, this assumption does not always hold, hence, introducing dependence in the collective model becomes a necessity. In this sense, one trend consists of assuming dependence between the number of claims and their average severity. Alternatively, we can consider heterogeneity between the individual cost of claims associated with a given number of claims. Using the Sarmanov distribution, in this paper we aim at introducing dependence between the number of claims and the individual claim severities. As marginal models, we use the Poisson and Negative Binomial (NB) distributions for the number of claims, and the Gamma and Lognormal distributions for the cost of claims. The maximum likelihood estimation of the proposed Sarmanov distribution is discussed. We present a numerical study using a real data set from a Spanish insurance portfolio.

Keywords: collective risk model; dependence; bivariate Sarmanov distribution; estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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