Claim dependence with common effects in credibility models

The credibility premiums for models with dependence induced by common effects

“…If we assume normal distributions to all the variables X ij , parameters Θ i , and the common effect Λ, then it is well known that the projection coincides with conditional expectation and, therefore, the credibility prediction is the same as the Bayes prediction (posterior expectation). Under the normality assumptions, Yeo and Valdez (2006) examined a much more…”

“…It appears, however, that in the context of credibility pricing, the dependence over individual risks has not received adequate attention from researchers and practitioners so far. The exception seems only Yeo and Valdez (2006), who proposed a rather special credibility model with claim dependence characterized by common effects (such as earthquake, common economic environment) and investigated the corresponding credibility premiums under normally distributed claim amounts.…”

“…In this paper, we aim at studying the Bühlmann and Bühlmann-Straub models with dependence structure that is characterized by a stochastic latent risk parameter (referred to as common effect, following the terminology of Yeo and Valdez (2006)). We establish the credibility formulae for the general credibility models with common effects.…”

TVaR-based capital allocation with copulas

“…However, it admits positive as well as negative dependence between a set of random variables. As said in Yeo and Valdez (2006) where the FGM copula is used to link claim variables in a credibility model, even if it can model only weak dependence, the FGM copula permits to assign a unique dependence parameter for each pair or group of risks and allows a more complex dependence structure than most of the copulas which use only one or few parameters. Furthermore, its handy form allows explicit calculus and thus exact results.…”

The credibility models with equal correlation risks

“…In fact, it has been recognized that there exist many important insurance scenarios where this classical assumption is violated; see, for example, [6][7], in which the random common effects were introduced to induce dependence and corresponding credibility estimators were derived. Actually, there have been many remarkable efforts in the existing actuarial literature to study the impacts of dependent risks in various aspects; see e.g., [8][9][10], etc.…”