We investigate the influence of the dependence between random losses on the shortfall and on the diversification benefit that arises from merging these losses.We prove that increasing the dependence between losses, expressed in terms of correlation order, has an increasing effect on the...

This paper focuses on techniques for constructing Bonus-Malus systems in third party liability automobile insurance. Specifically, the article presents a practical method for constructing optimal Bonus-Malus scales with reasonable penalties that can be commercially implemented. For this purpose,...

Actuaries intuitively feel that positive correlations between individual risks reveal a more dangerous situation compared to independence. The purpose of this short note is to formalize this natural idea. Specifically, it is shown that the sum of risks exhibiting a weak form of dependence known...

This paper examines an integrated ratemaking scheme including a priori risk classification and a posteriori experience rating. In order to avoid the high penalties implied by the quadratic loss function, the symmetry between the overcharges and the undercharges is broken by introducing...

The aim of this paper is to apply the method proposed by Denuit, Genest andMarceau (1999) for deriving stochastic upper and lower bounds on the present value of a sequence of cash flows, where the discounting is performed under a given stochastic return process. The convex approximation provided...

Premiums and benefi ts associated with traditional life insurance contracts are usually specifi ed as fi xed amounts in policy conditions. However, reserve-dependent surrender values and reserve-dependent expenses are common in insurance practice. The famous Cantelli theorem in life insurance...

In this paper, we extend the concept of mutual exclusivity proposed by Dhaene and Denuit (1999) to its tail counterpart and baptise this new dependency structure as tail mutual exclusivity. Probability levels are first specified for each component of the random vector. Under this dependency...