B1854
Title: Collective risk models with FGM dependence
Authors: Helene Cossette - Laval University (Canada) [presenting]
Abstract: Collective risk models, in which the aggregate claim amount of a portfolio is defined in terms of as a sum of a random number (frequency) of random claim amounts (severities), play a crucial role. In these models, the classical approach is to assume that the random number of claims and their amounts are independent, even if this might not always be the case. A class of collective risk models is considered, in which the dependence structure of the random number of claims and the individual claim amounts is defined in terms of multivariate Farlie-Gumbel-Morgenstern (FGM) copula. By leveraging a one-to-one correspondence between the family of FGM copulas and the family of multivariate symmetric Bernoulli random vectors, closed-form expressions are found for the moments and Laplace-Stieltjes transform of the aggregate claim amount. The dependence properties of the proposed class of collective risk models are examined. Even if the Farlie-Gumbel-Morgenstern copula may only induce moderate dependence, it is shown through numerical examples that the cumulative effect of dependence can generate large ranges of values for the expectation, the variance, and risk measures (such as the tail-value-at-risk and the entropic risk measure) of the aggregate claim amount. Applications of the proposed class of collective risk models are presented in various contexts of non-life insurance.
