The 2015 Risk and Stochastics Conference will take place on Wednesday 22 and Thursday 23 April 2015. This conference celebrates the 70th year of Professor Ragnar Norberg and acknowledges his academic achievements; in particular, his legacy at LSE, which is primarily but note solely due to the Risk and Stochastics enterprise, which he was instrumental in founding and which has conspicuously placed the School on the world map in the areas of modern actuarial and financial mathematics and their interface.
The speakers at this conference are contemporaries and long-standing associates of Ragnar and offer insights gained from many years of experience and expertise.
Venue:
Royal Statistical Society
12 Errol Street
London
EC1Y 8LX
This conference is organised and funded by the Department of Statistics at the London School of Economics (LSE)
IMPORTANT NOTICE: If you have registered to attend this conference using EShop but have not received an email from our research administrator Ian Marshall, please contact him at this address: i.marshall@lse.ac.uk.
Odd Olai Aalen
University of Oslo
Title: Causal inference and survival analysis: a new look at old tools
Abstract: The modern development of causal inference has implications for survival analysis. The implicit conditioning on survival which is present in the definition of intensity processes and hazard rates opens for collider effects. We shall look at the implications of this. The causal viewpoint also inspires a closer look at the censoring concept.
The idea of local independence is now gaining a stronger foothold through the work of Vanessa Didelez and Kjetil Røysland. The latter author in an elegant paper combines martingales, counting processes, local independence and marginal structural models. Local independence is a key concept in understanding causal inference for processes.
Mediation is an important topic in causal inference, and we shall briefly consider this in a process setting
Knut Kristian Aase
Norwegian School of Economics
Title: What type of pensions would most people prefer?
(Life insurance and pension contracts II: the life cycle model with recursive utility)
Abstract: I analyse optimal consumption and pension insurance during the life time of a consumer using the life cycle model, when the consumer has recursive utility. The relationship between substitution of consumption and risk aversion is highlighted and clarified by the introduction this type of preferences. I illustrate how recursive utility can be used to mitigate the empirical consumption puzzle for aggregates. This indicates a plausible choice for the parameters of the utility function, relevant for the consumer in the life cycle model. A major finding is that it is optimal for the insurance buyer to smooth adverse shocks to the market, unlike what the conventional model predicts. This has implications for the life and pension insurance industry.
Søren Asmussen
Aarhus University
Title: Exponential family techniques in the lognormal left tail, with applications to portfolio VaR
Abstract: Sums S_n=X_1+...+X_n of lognormals arises in a wide variety of disciplines such as engineering, economics, insurance or finance, and are often employed in modelling across the sciences. The right lognormal tail P(S_n>y) is heavy-tailed and typically analysed by subexponential techniques. The left tail P(S_n<z) is of interest for example in portfolio VaR calculations. The typical tool would be applying saddlepoint or large deviations techniques. This faces, however, the problem that the Laplace transform L(\theta)=Ee^{-\theta X} is not explicit. We present an approximation for L(\theta) in terms of the Lambert W function. This is used to describe the shape of the exponentially tilted distribution \tilde P(X\in dx)=e^{-\theta x}P(X\in dx)/L(\theta) and to derive a saddlepoint type approximation for P(S_n<z). Also related importance sampling algorithms are presented. Numerical examples are presented in a range of parameters that we consider realistic for portfolio VaR calculations.
The talk is based on joint work with Jens Ledet Jensen and Leonardo Rojas-Nandaya
Nick Bingham
Imperial College London
Title: The work of Ragnar Norberg
Abstract: Ragnar Norberg has been an influential scholar over many years now, in his research, his teaching and his personal influence. We give a (necessarily selective) overview of some of his many achievements.
Tomas Björk
Stockholm School of Economics
Title: Dynamic equilibrium models with time inconsistent preferences
Abstract: In this talk we give an overview of some recent work on general equilibrium models in continuous time, where the agents have preferences which in various ways are time inconsistent. In particular we study how time inconsistent preferences affect the equilibrium stochastic discount factor and the equilibrium short rate.
The talk is partly based on joint work with Mariana Khapko.
Freddy Delbaen
ETH Zürich
Title: Monetary utility functions with the CxLS (convex level sets) property
Abstract: Monetary utility functions are -- except for the expected value -- not of von Neumann-Morgenstern type. In case the utility function has convex level sets in the set of probability measures on the real line, we can give some characterisation that comes close to the vN-M form. For coherent utility functions this was solved by Ziegel. The general concave case under the extra assumptions of weak compactness, was solved by Stephan Weber. In the general case the utility functions are only semi continuous. Using the fact that law determined utility functions are monotone with respect to convex ordering, we can overcome most of the technical problems. The characterisation is similar to Weber's theorem except that we need vN_M utility functions that take the value $-\infty$. Having convex level sets can be seen as a weakened form of the independence axiom in the vN-M theorem.
Joint work with Fabio Bellini, Valeria Bignozzi and Johanna F Ziegel.
Hans Föllmer
Humboldt University of Berlin
Title: Mathematical aspects of systemic risk
Abstract: We discuss some mathematical aspects of systemic risk in large financial networks, in particular the interplay between local and global risk analysis in terms of convex risk measures.
Christian Hipp
Karlsruhe Institute of Technology
Title: Optimal control forinsurers: the bivariate case
Abstract: A variety of univariate control problems with application in insurance is solved now, in the sense that solvability of Hamilton-Jacobi-Bellman (HJB) equations and its numerical solutions are well understood. These control problems are univariate in the sense that they have HJB equations which are based ordinary differential equations. The talk is concerned with control problems for which the HJB equation is based on a differential equation in two variables. Such cases show up when the time horizon is finite (time as a second variable), or when the risk process is bivariate Markov (which typically happens in mixture models after Markovisation).
This covers the following kind of problems:
a) minimizing finite time ruin probability with investment or with excess of loss reinsurance, for a classical Lundberg risk model;
b) minimizing infinite time ruin probability for a modulated Markov risk process in which the random intensity is not observable, again with control of investment or of reinsurance;
c) optimal dividend payment with a ruin constraint (where the instantaneous ruin probability is the second variable).
The talk is on work in progress.
Monique Jeanblanc
University of Évry Val d'Essonne
Title: Enlargement of filtration in a discreet time setting
Abstract: We study enlargement of filtration for a discrete time process. In that case, all the results are simple and do not require abstract assumptions, contrary to continuous time setting. We shall give the proofs and indicate the relationship with classical results of Marc Yor, Thierry Jeulin and Jean Jacod.
(This title and abstract was updated on 17 April 2015)