Série de conférence de Pierre Del Moral (INRIA Bordeaux) Jeudi 19 octobre / Thursday, October 19 15h30 / 3:30 pm CRM Pavillon André-Aisenstadt Université de Montréal salle 6254

Particle methodologies: A bridge across mathematics, physics, biology and information theory

In the last three decades, there has been a dramatic increase in the use of Feynman-Kac type particle methods as a powerful tool in applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. The particle simulation techniques they suggest are also called “resampled and diffusion Monte Carlo methods” in quantum physics, “genetic and evolutionary type algorithms” in computer science, “sequential Monte Carlo methods” in Bayesian statistics, and “particle filters” in advanced signal processing. These mean field type particle methodologies are used to approximate a flow of probability measures with an increasing level of complexity. This class of probabilistic models includes conditional distributions of signals with respect to noisy and partial observations, non-absorption probabilities in Feynman-Kac-Schrödinger type models, Boltzmann-Gibbs measures, as well as conditional distributions of stochastic processes in critical regimes, including quasi-invariant measures and ground state computations. In this public lecture, I will present a pedagogical introduction to the stochastic modeling and the theoretical analysis of these sophisticated probabilistic models. I will discuss the origins and the mathematical foundations of these particle stochastic methods, as well as their applications in rare event analysis, signal processing, mathematical finance, and Bayesian statistical inference.

La conférence sera suivie d’un vin d’honneur servi au Salon Maurice-l’Abbé.

---

Vendredi 20 octobre / Friday, October 20
13h30 / 1:30 pm

Venue
HEC Montréal
3000, Chemin de la Côte-Sainte-Catherine
Salle Société canadienne des postes (1er étage, section jaune)

On the stability and the uniform propagation of chaos properties of Ensemble Kalman-Bucy

The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field McKean-Vlasov type particle interpretation of the Kalman-Bucy difusions. In contrast to more conventional particle filters and nonlinear Markov processes these models are designed in terms of a diffusion process with a diffusion matrix that depends on particle covariance matrices. Besides some recent advances on the stability of nonlinear Langevin type diffusions with drift interactions, the long-time behaviour of models with interacting diffusion matrices and conditional distribution interaction functions has never been discussed in the literature. One of the main contributions of the talk is to initiate the study of this new class of models. The talk presents a series of new functional inequalities to quantify the stability of these nonlinear diffusion processes. In the same vein, despite some recent contributions on the convergence of the Ensemble Kalman filter when the number of sample tends to infinity very little is known on stability and the long-time behaviour of these mean-field interacting type particle filters. The second contribution of this talk is to provide uniform propagation of chaos properties as well as Lp-mean error estimates w.r.t. to the time horizon. Our regularity condition is also shown to be sufficient and necessary for the uniform convergence of the Ensemble Kalman filter. The stochastic analysis developed in this talk is based on an original combination of functional inequalities and Foster-Lyapunov techniques with coupling, martingale techniques, random matrices and spectral analysis theory.

Roger M. Cooke (Resources for the Future, Washington, DC and Technische Universiteit Delft, The Netherlands) Mercredi 18 octobre / Wednesday, October 18, 2017 19h30 / 7:30 CRM Pavillon André-Aisenstadt, Université de Montréal, room 1140

The Confidence Trap : Dysfunctional Dialogues about Climate

Mutilation of facts, scriptural snake oil, gerrymandering the proof burden, bloated overconfidence and outright lies – these are among the miasmas fouling the public debate about climate change. The surprise is not that people try these stratagems, but that they are successful. A snarly cognitive illusion is preventing us from dealing rationally with climate uncertainties (a cognitive illusion is like an optical illusion involving the brain instead of the eyes). After a "syllabus of errors", this talk will focus on better ways to capture and incorporate expert's judgments on climate change. Developed in quantitative risk analysis, structured expert judgment has been used in a wide range of applications from nuclear safety, public health, investment banking to policy analysis and natural hazards. It is now poised to enter the climate debate in earnest. Can it help? It's time to find out.

Peter Raupach (Deutsche Bundesbank) Lundi 25 septembre / Monday, September 25, 2017 12h00 / 12:00 p.m. CIRANO 1130, rue Sherbrooke Ouest, 14e étage (métro Peel)

Centrality-based Capital Allocations

In this talk, I will describe the effect of capital rules on a banking system that is connected through correlated credit exposures and interbank lending. Keeping total capital in the system constant, the reallocation rules, which combine individual bank characteristics and interconnectivity measures of interbank lending, are to minimize a measure of system-wide losses. Using the detailed German Credit Register for estimation, we will see that capital rules based on eigenvectors dominate any other centrality measure, saving about 15% in expected bankruptcy costs. This benefit is not overwhelming but a first proof that the approach can work in general. In exercises like ours, it is essential to combine the contagion model with a proper model for the exogenous shocks that hit the system, mainly for the following reason. If a bank defaults due to extreme loan losses in the real sector, other banks tend to have similar problems. This will erode their capital and so harm their ability to absorb losses from interbank lending. If this simple mechanism is neglected, financial networks may appear much more stable than they really are. This talk is based on joint work with Adrian Alter (IMF) and Ben Craig (Fed Cleveland).

Michel M. Dacorogna (DEAR-Consulting, Switzerland) Mercredi 13 septembre / Wednesday, September 13, 2017 19h30 / 7:30 pm HEC Montréal Pavillon Decelles, 5255, avenue Decelles (métro Côte-des-Neiges) Amphithéâtre Lévis, section sud, 3e étage

A Change in Paradigm for the Insurance Industry

In this presentation, I will review changes in the insurance industry due to new risk-based regulations such as Solvency 2 and SST and pressure of the shareholders. The move from corporate management based on cash-flow to risk-based management will be described and discussed through its consequences on capital management, economic valuation and the internal model. I will also discuss the limits and difficulties of Enterprise Risk Management and its effect on the organization of companies. Moreover, I will emphasize the changing role of actuaries in insurance. As we will see, the risk/return relationship is becoming a central element of the company's management, slowly supplanting the traditional accounting view.

Paul Embrechts (ETH Zürich) Lundi 11 septembre / Monday, September 11, 2017 19h30 / 7:30 pm HEC Montréal Pavillon Decelles, 5255, avenue Decelles (métro Côte-des-Neiges) Salle Sept-Îles, section nord, 3e étage

Risk Management: Then, Now and Tomorrow

The regulatory landscape is undergoing considerable changes worldwide. The 2007–2009 Financial Crisis brought into question several aspects of regulation for banking, the so-called Basel and Solvency guidelines. At the same time, demographic and economic developments (e.g., longevity, low interest rates) are causing major problems for the insurance industry, and this mainly, but not exclusively, for life insurance. Added to these we do witness important changes to society at large, also driven by information technology. Besides the obvious social and political changes experienced worldwide, we should add more technologically driven ones like network vulnerability and systemic risk, new products, large data (data science, machine learning), block-chain technology, and cyber security. These developments will no doubt have a considerable impact on the financial and insurance industry both at the business as well as at the regulatory level. In this talk I will discuss some of the underlying issues from a more personal perspective as a researcher in Quantitative Risk Management.