Actuarial comparisons for aggregate claims with randomly right-truncated claims

How retention levels influence the variability of the total risk under reinsurance

“…The next result follows the spirit of Theorem 4.4 in Escudero and Ortega (2008) by taking the function h 1 (x) = U + x instead of h 2 (x) = Ux.…”

“…Recently, the impact of catastrophic events on insurance companies solvencies led to the insurance industry to call for some form of government assistance, such as a kind of excess-loss contracts, where the trigger levels are set at a level above the layers of reinsurance being provided in the private markets. In this context, Escudero and Ortega (2008) have considered an extension of LCR and excess-loss treaties with arbitrary random retention levels. They consider that each individual claim exceeding its random threshold is eliminated from the insurer's account and ceded to reinsurers; thus the retained total claim amount is a random linear combination of Bernoulli random variables with parameter given by the distribution function of the individual claim sizes.…”

“…By following the framework in Escudero and Ortega (2008), we consider stochastic retention levels and their dependencies that are modeled by some integral dependence orderings (see Denuit and Müller 2002). We obtain conditions for the increasing convex order (also known as stop-loss order and variability order, see Stoyan 2002 andShanthikumar 2007) to hold.…”

Variability comparisons for some mixture models with stochastic environments in biosciences and engineering

“…In particular, variability bounds are instruments for risk analysis in financial insurance portfolios (see, for instance, Goovaerts et al 2000;Kaas et al 2000;Genest et al 2002). Some multivariate extensions of the increasing convex order have been used recently to study the influence of stochastic dependencies on some mixtures defined by functionals of random variables (see Escudero and Ortega 2008;Fernández-Ponce et al 2008;Ortega and Escudero 2008). In this paper, we will use the increasing (decreasing) directionally convex order (see Shaked and Shanthikumar 2007) to compare the dependence between the stochastic environments.…”

“…We recall this concept, introduced in Shaked and Shanthikumar (1990), also studied by Meester and Shanthikumar (1993;1999) and Chang et al (1994). Recent applications can be seen in Escudero and Ortega (2008) and Fernández-Ponce et al (2008).…”