This paper studies a new risk measure derived from the expected area in red introduced in Loisel (2005). Specifically, we derive various properties of a risk measure defined as the smallest initial capital needed to ensure that the expected time-integrated negative part of the risk process on a...

We consider the classical risk model and carry out a sensitivity and robustness analysis of finite-time ruin probabilities. We provide algorithms to compute the related influence functions. We also prove the weak convergence of a sequence of empirical finite-time ruin probabilities starting from...

In the renewal risk model, several strong hypotheses may be found too restrictive to model accurately the complex evolution of the reserves of an insurance company. In the case where claim sizes are heavy-tailed, we relax the independence and stationarity assumptions and extend some asymptotic...

The present paper aims to point out how the stationary-excess operator and its iterates transform s-convex stochastic orders and the associated moment spaces. This allows us to propose a new unified method on constructing s-convex extrema for distributions that are known to be t-monotone. Both...

In the classical risk model, we prove the weak convergence of a sequence of empirical finite-time ruin probabilities. In an earlier paper (see Loisel et al., (2008)), we proved an equivalent result in the special case where the initial reserve is zero, and checked that numerically the general...

We present a new model of loss processes in insurance. The process is a couple (N,L) where N is a univariate Markov-modulated Poisson process (MMPP) and L is a multivariate loss process whose behavior is driven by N. We prove the strong consistency of the maximum likelihood estimator of the...