In this paper we focused our attention to the study of an excess of loss reinsurance with reinstatements, a problem previously studied by Sundt [5] and, more recently, by Mata [4] and HÄurlimann [3]. As it is well-known, the evaluation of pure premiums requires the knowledge of the claim size...

In this paper we consider the problem of studying the gap between bounds of risk measures for sums of non-independent random variables. Owing to the choice of the context where to set the problem, namely that of distortion risk measures, we first deduce an explicit formula for the risk measure...

This paper studies excess of loss reinsurance with reinstatements in the case in which the aggregate claims are generated by a discrete distribution, in the framework of risk adjusted premium principle. More precisely, after the attention is focused on conditions ensuring feasibility of initial...

This paper studies excess of loss reinsurance with reinstatements in the case in which the aggregate claims are generated by a discrete distribution, in the framework of risk adjusted premium principle. By regarding to comonotonic exchangeability, a generalized definition of initial premium is...

This paper studies excess of loss reinsurance with reinstatements in the case in which the aggregate claims are generated by a discrete distribution, in the framework of risk adjusted premium principle. By regarding to comonotonic exchangeability, a generalized definition of initial premium is...

In this paper we consider the problem of determining approximations for distortion risk measures of sums of non-independent random variables. First, we give an overview of the recent actuarial literature on distortion risk measures and convex bounds for sums of random variables. Then, we examine...

Recently in actuarial literature several authors have derived lower and upper bounds in the sense of convex order for sums of random variables with given marginal distributions and unknown dependency structure. In this paper, we derive convex bounds for sums of non-independent and identically...