**CLAUDE 2016 CONFERENCE**

On September 5^{th}, 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.

With the financial support of department of mathematics of

and

of Université Lille 1.

## Registration is free but compulsory. Participants may register either for Claude 2016 conference only or for both Claude 2016 event and EAJ conference at the same time.

**Programme**

8:45

*Welcome coffee*

9:30 – 9:50

Welcome address

9:50 – 10:40

Michel DENUIT – dBivariate higher-order increasing convex orders and related dependance concepts, with applications to risk and insurance

10:40

*Coffee break*

11:10 – 12:00

Frank BALL – Susceptibility sets and the final outcome of stochastic SIR epidemic models

12:00 – 12:50

Sergey UTEV – « Non-ruin Hamiltonian Transform Operator »

12:50

*Lunch break*

14:00 – 14:50

Dimitrios KONSTANTINIDES – Asymptotic ruin probabilities for a multidimensional renewal risk model with multivariate regularly varying claims

14:50 – 15:40

Mercè CLARAMUNT – Discrete Schur-constant models in insurance

15:40

*Refreshment break*

16:10 – 17:00

Andre de PALMA – Economic distributions and primitive distributions in industrial organization and international trade

17:00 – 18:30

Surprise activity

18h30 – 23:00

*Closing Cocktail of C.Lefèvre Day & Welcome cocktail of EAJ2016 conference*

**Confirmed invited speakers**

FRANK BALL

*Univ. of Nottingham*

Frank Ball has a BSc in Mathematics from the University of Manchester, a Diploma in Mathematical Statistics from the University of Cambridge anda DPhil in Biomathematics from the University of Oxford. He has been Professor of Applied Probability at the University of Nottingham since

1993 and is currently on the editorial boards of Mathematical Biosciences, Mathematical Medicine and Biology and the Scandinavian Journal of Statistics.

**Susceptibility sets and the final outcome of stochastic SIR epidemic models**

*Frank Ball (University of Nottingham)*

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 of a 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 Lef`evre and Philippe Picard.

MERCE CLARAMUNT

*Univ. of Barcelona, Spain*

M. Mercè Claramunt Bielsa is actuary and has a PhD in Economics from the Universitat de Barcelona. She is associate professor at the Departament de Matemàtica Econòmica, Financera i Actuarial of the Universitat de Barcelona. She is the main researcher of the Actuarial and Financial Modelling research group (2014SGR152). She is also the research coordinator of the ICEA-UB founded chair on Insurance and pension funds.

**Discrete Schur-Constant Models in Insurance**

*Mercè Claramunt (University of Barcelona)*

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.profe

MICHEL DENUIT

*Univ. of Louvain, Belgium*

Michel Denuit got a Master’s degree in Mathematics, a Master’s degree in Actuarial Science and a PhD degree in Statistics, all from ULB (Brussels, Belgium).

He devoted all his career to teaching and research in actuarial science, at UCL (Louvain-la-Neuve, Belgium) where he is professor in the Institute of Statistics, Biostatistics and Actuarial Science. He serves as Director of the UCL Master in Actuarial Science.

He has held several visiting appointments at universities and research institutes, including the Centre for Risk and Insurance Studies of the KULeuven (Leuven, Belgium), the Department of Actuarial Science of the University of Lausanne (Switzerland), the Institute for Finance and Insurance of the Lyon 1 University (ISFA, Lyon, France), and the National Institute of Statistics and Applied Economics of Rabat (INSEA, Rabat, Marocco).

He has done extensive research in the areas of mathematical risk theory and actuarial pricing. He specialized in applying advanced probabilistic and statistical methods to solve actuarial problems.

He conducted several projects with major European (re)insurance companies and banks. He has served as Director of the UCL Institute of Statistics, as well as on several professional actuarial committees in Belgium and in the EU.

**Bivariate higher-order increasing convex orders and related dependence concepts,**

**with applications to risk and insurance**

*Michel Denuit (University of Louvain)*

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).

ANDRE DE PALMA

*NS Cachan, France*

André de Palma holds a PhD in Physics (1981), under the supervision of Nobel Prize Y. Prigogine, (1981, Free University of Brussels), and a PhD in Economics (1988, University of Bourgogne). He is specialized in Transportation and Urban Economics, Industrial Organization, Decision theory (discrete choice models).

André de Palma has been teaching and conducting research at The Free University of Brussels, McMaster University, Queen’s University, Northwestern University, University of Geneva, University of Cergy-Pontoise, and Ecole Poytechnique. He is currently teaching at Ecole Normale Supérieure de Cachan / University Paris-Saclay, in Paris. He has published more than 250 articles (including in Econometrica, American Economic Review, RAND, Review of Economics Studies, Transportation Science, and Journal of Public Economics), and 7 books.

With Claude Lefèvre, Simon Anderson and Jacques Thisse, he has developed research on the foundation of discrete choice models, since the late 70’s. These models have influenced the development of the “new industrial organization”.

With Claude Lefèvre, Moshe Ben-Akiva, Richard Arnott and Robin Lindsey, he has set the basis of dynamic models in transportation, which revolutionize private transport modelling. He has developed, with Yurii Nesterov, a fully dynamic congestion software: METROPOLIS.

With Nathalie Picard, he has developed two websites to study experimentally risk attitude of individual and couples. Together, they have developed a software, RiskTolerance, based on advanced econometric methods. They are partner of RiskDesign which market RiskTolerance used by several major banks and insurance companies in France.

**Economic distributions and primitive distributions in Industrial Organization and International Trade**

*André de Palma (with Simon Anderson)*

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.

DIMITRIOS KONSTANTINIDES

*Univ. of the Agean, Greece*

Dimitrios G. Konstantinides was born in Thessaloniki where he had his elementary education. Later he continued in gymnasium in Larissa and he finished the lyceum in Athens at Kalithea. After entrance exams he became student of the Department of Mathematics in University of Athens. For his M.Sc. degree he went to Kiev at the Mechaniko-Mathematical Department of the Kiev National University named after Shevtshenko. Next for his doctoral studies he entered to the Mechaniko-Mathematical Department of the Moscow State University named after Lomonossov. He began his academic career in Technical University of Crete for six years where he taught to students of the Department of Electrical Engineering and Computer Science and of the Department of Industrial and Management Engineering. Then he continued to the University of the Aegean at the Department of Mathematics and the Department of Statistics and Actuarial Science.

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

*Dimitrios G. Konstantinides (University of the Agean)*

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 dierent 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.

SERGEY UTEV

*Univ. of Leicester, UK*

Sergey Utev is Professor at the Department of Mathematics, Leicester University; He used to work at Nottingham University, Australian National University (Canberra), La Trobe University (Melbourne), Sobolev Institute of Mathematics (Novosibirsk). He also had several long visiting positions to Université Libre De Bruxelles, University of Groningen, University of Zurich.

**Non-ruin Hamiltonian Transform Operator**

*Sergey Utev (UNversity of Leicester)*

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.

**Venue**

ISFA, Université Lyon 1, 50 avenue Tony Garnier, 69007 Lyon, France

**Homepage:** http://eaj2016.org/index.php/claude2016/

**Scientific Committee**

Stéphane Loisel (ISFA, Univ. Lyon 1)

Pierre Patie (Cornell & ULB)

Yahia Salhi (ISFA, Univ. Lyon 1)

Thomas Simon (Univ. Lille 1)

Julien Trufin (ULB)

**Local organizing Committee**

Sophie Castelbou

Anne Eyraud-Loisel

Laurent Gondy

Stéphane Loisel

Carol Nérieux

Yahia Salhi

**Organizers**

- Institut de Science Financière et d’Assurance (ISFA, Université Lyon 1)
- Université Libre de Bruxelles
- Institut des Actuaires (IA)