Asymptotic multivariate finite-time ruin probabilities with heavy-tailed claim amounts: Impact of dependence and optimal reserve allocation

International audienceIn ruin theory, the univariate model may be found too restrictive to describe accurately the complex evolution of the reserves of an insurance company. In the case where the company is composed of multiple lines of business, we compute asymptotics of finite-time ruin probabilities. Capital transfers between lines are partially allowed. When claim amounts are regularly varying distributed, several forms of dependence between the lines are considered. We also study the optimal allocation of a large global initial reserve in order to minimize the asymptotic ruin probability

SYMMETRY AND INTERPOLATION OF ESTIMATES FOR THE COMPLEX GREEN OPERATOR (Topology of pseudoconvex domains and analysis of reproducing kernels)

This note is a summary of a lecture on the results of [8] about estimates for the complex Green operator, given by the author in the occasion of the conference: “Topology of pseudoconvex domains and analysis of reproducing kernels” on November 20-22nd, 2017, in RIMS, Kyoto, Japan. The results of this note are contained in [7] and [8]

Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation

In the renewal risk model, we study the asymptotic behavior of the expected time-integrated negative part of the process. This risk measure has been introduced by Loisel (2005). Both heavy-tailed and light-tailed claim amount distributions are investigated. The time horizon may be finite or infinite. We apply the results to an optimal allocation problem with two lines of business of an insurance company. The asymptotic behavior of the two optimal initial reserves are computed.Ruin theory; heavy-tailed and light-tailed claim size distribution; risk measure; optimal reserve allocation

Asymptotic Finite-Time Ruin Probabilities for a Class of Path-Dependent Heavy-Tailed Claim Amounts Using Poisson Spacings

In the compound Poisson risk model, several strong hypotheses may be found too restrictive to describe accurately the evolution of the reserves of an insurance company. This is especially true for a company that faces natural disaster risks like earthquake or flooding. For such risks, claim amounts are often inter-dependent and they may also depend on the history of the natural phenomenon. The present paper is concerned with a situation of this kind where each claim amount depends on the previous interclaim arrival time, or on past interclaim arrival times in a more complex way. Our main purpose is to evaluate, for large initial reserves, the asymptotic finite-time ruin probabilities of the company when the claim sizes have a heavy-tailed distribution. The approach is based more particularly on the analysis of spacings in a conditioned Poisson process.Risk process; finite-time ruin probabilities; asymptotic approximation for large initial reserves; path-dependent claims, heavy-tailed claim amounts; Poisson spacing;