CLAUDE 2016 CONFERENCE

On September 5th, an academic research day (9a.m.-7p.m.) is organized on the occasion of the emeritus status of Prof. Claude Lefèvre (ULB and ISFA). It is a satellite event of the 2016 EAJ Conference and is organized at the same venue (ISFA). Claude has just become emeritus professor at Université Libre de Bruxelles, and continues to teach and do research at ISFA. This one-day event will feature serious academic talks, less serious short talks (with or without pictures/videos of Claude), as well as a surprise activity (from 6p.m. to 7p.m.). It will be concluded by a cocktail (7:30p.m.-9:30p.m.) that coincides with the welcome cocktail of the EAJ Conference.

Confirmed invited speakers

Abstract : Susceptibility sets and the final outcome of stochastic SIR epidemic models

This talk is concerned with exact results for the final outcome (total size and severity) of stochastic SIR (susceptible → infective → removed) epidemics among a closed, finite population. The concept ofa susceptibility set is introduced and shown to be intimately related to factorial moments of the number of initial susceptibles who ultimately avoid infection. This connection leads to new, probabilistically illuminating proofs of exact results concerning the final outcome of collective Reed–Frost epidemic processes, in terms of Gontcharoff polynomials, first obtained using martingale techniques in a series of papers by Claude Lefèvre and Philippe Picard.

Abstract : Discrete Schur-Constant Models in Insurance

In this talk we introduce a class of Schur-constant survival models, of dimension n, for arithmetic non-negative random variables. The talk is based on Castañer, Claramunt, Lefèvre and Loisel (2015). After some preliminaries related with the continuous case, the discrete model is defined through a univariate survival function that is shown to be n-monotone. Correlation measures are derived and some specific models are commented. Three processes in insurance theory are discussed for which the claim interarrival periods form a Schur-constant model.

Abstract : Bivariate higher-order increasing convex orders and related dependence concepts, with applications to risk and insurance

In this talk, we discuss dependence concepts related to the bivariate (1,2)- and (2,1)-increasing convex orders introduced by Denuit, Lefevre and Mesfioui (1999) and further studied by several authors, including Denuit and Eeckhoudt (2010) and Denuit and Mesfioui (2010). These notions appropriately weaken the quadrant dependence and supermodular dominance.
Several applications are discussed, including the composition of an optimal portfolio (Denuit and Eeckhoudt, 2016), risk aversion with two risks (Li et al., 2016) and the amount of information contained in signals (Denuit, 2010, Denuit and Trufin, 2016).

Abstract : Economic distributions and primitive distributions in Industrial Organization and International Trade

We link fundamental technological and taste distributions to endogenous economic distributions of firm size (output, profit) and prices in extensions of canonical IO and Trade models. We provide constructive proofs to recover the demand structure, mark-ups, and distributions of cost, price, output and profit from just two of the distributions (or from demand and one distribution). For CES, all distributions lie in the same family (e.g., the “Pareto circle”). The circle is broken by introducing quality. We extend our general analysis, modeling the technological relation between quality and cost to link two distribution groups (output, profit, and quality-cost; price and cost). The distributions of output, profit, and prices suffice to recover the cost distribution, the demand form, and the quality-cost relation. A continuous logit demand model illustrates: exponential (resp. normal) quality-cost distributions generate Pareto (log-normal) economic size distributions. Pareto prices and profits are reconciled through an appropriate quality-cost relation. We also find long-run equilibrium distributions.

Abstract : Asymptotic Ruin Probabilities for a Multidimensional Renewal Risk Model with Multivariate Regularly Varying Claims

This paper studies a continuous-time multidimensional risk model with constant force of interest and dependence structures among random factors involved. The model allows a general dependence among the claim-number processes from di
erent insurance businesses. Moreover, we utilize the framework of multivariate regular variation to describe the dependence and heavytailed nature of the claim sizes. Some precise asymptotic expansions are derived for both nitetime and innite-time ruin probabilities.

Astract : Non-ruin Hamiltonian Transform Operator

A standard Hamiltonian Path integrals and/or path calculations technique is modified to compute the finite time nonruin probability. The focus is on the numerical computations.
Although the approach is well known in the quantum mechanics, the applications to Finance and Actuarial Sciences are  still scattered.
The Transform of the Levy type Hamiltonians, which corresponds to the ruin probability, is constructed and referred  to as the Non-ruin Hamiltonian transfer operator.
The operator is related to the Nagaev transform of the transfer operator, found to be useful in tackling the Gaussian Approximation and the Large Deviation Principle for Markov processes.