The following seminars have been jointly organised by the Risk and Stochastics Group and the Department of Mathematics. The Seminar normally takes place bi-weekly on Thursdays from 12.00 - 13:00, unless stated below. The series aims to promote communication and discussion of research in the mathematics of insurance and finance and their interface, to encourage interaction between practice and theory in these areas, and to support academic students in related programmes at postgraduate level. All are welcome to attend. Please contact Enfale Farooq, the Research Manager, on E.Farooq@lse.ac.uk for further information about any of these seminars.
Thursday 2 December 2021 - Christian Furrer (University of Copenhagen)
12:00 on Zoom - register here
Change of measure techniques for scaled insurance cash flows
Incidental policyholder behaviour, including free policy conversion and stochastic retirement, may have a significant impact on the market value of a life insurance contract; consequently, models should account for this. However, the inclusion of incidental policyholder behaviour typically leads to duration effects and thus an increase in computational complexity. In this talk, I show how change of measure techniques can be used to conveniently deal with this added layer of complication.
Previous seminars in the series:
Thursday 18 November 2021 - Xiaoli Wei (TBSI)
Cooperative multi-agent reinforcement learning: A mean field perspective
Multi-agent reinforcement learning (MARL) has enjoyed substantial successes in many applications including real-time resource allocation, order matching for ride-sharing, and autonomous driving. Despite the empirical success of MARL, general theories behind MARL algorithms are less developed due to the intractability of interactions, complex information structure, and the curse of dimensionality. Instead of directly analyzing the multi-agent systems, mean-field theory provides a powerful approach to approximate the games under various notions of equilibria. Moreover, the analytical feasible framework of mean-field theory leads to efficient and tractable learning algorithms with theoretical guarantees.
In this talk, we will demonstrate how mean-field theory can contribute to analyzing a class of simultaneous-learning-and-decision-making problems under cooperation, with unknown rewards and dynamics. Moreover, we will show that the learning procedure can be further decentralized and scaled up if a network structure is specified. Our result lays the first theoretical foundation for the so-called "centralized training and decentralized execution" scheme, a widely used training scheme in the empirical works of cooperative MARL problems. This is based on joint work with Xin Guo (Berkeley), Haotian Gu (Berkeley) and Renyuan Xu (University of Southern California).
Tuesday 9 November 2021 - Mike Lipkin (NYU)
Time Scales in Finance - Introducing event-driven finance to graduate students
In classical finance statistical noise is introduced to drive stock dynamics and quantify option pricing. This means the stock sits in a "heat bath". But much of actual trading concerns itself with events, such as take-overs, earnings announcements, etc. Such an event introduces a singularity into the pricing kernel. And mesoscopic quantities, such as volatility, become irrelevant or misleading. Here we look at a spectrum of events and see how they manifest themselves in time and pricing.
Thursday 21 October - Philippe Casgrain (ETH Zürich)
Anytime-valid sequential testing for elicitable functionals via supermartingales
We consider the problem of testing statistical hypotheses and building confidence sequences for elicitable and identifiable functionals, a broad class of statistical quantities which are of particular interest in the field of quantitative risk management. Assuming a framework in which data is collected sequentially, where a user may choose to accept or reject a hypothesis at any point in time, we provide powerful distribution-free and anytime-valid testing methods which rely on controlled supermartingales. Leveraging tools from online convex optimization, we show that tests can be optimized to improve their statistical power, with asymptotic guarantees for rejecting false hypotheses. By "inverting the test", these methods are extended to the task of confidence sequence building. Lastly, we implement these techniques on a range of examples to demonstrate their effectiveness.
Thursday 7 October - Birgit Rudloff (Vienna University of Economics and Business)
Epic Math Battles: Nash vs. Pareto
Nash equilibria and Pareto optimization are two concepts when dealing with multiple criteria. It is well known that the two concepts do not coincide. However, in this work we show that it is possible to characterize the set of all Nash equilibria for any non-cooperative game as the Pareto optimal solutions of a certain vector optimization problem. To accomplish this task, we enlarge the objective function and formulate a non-convex ordering cone under which Nash equilibria are Pareto efficient. We demonstrate these results, first, for shared constraint games in which a joint constraint is applied to all players in a non-cooperative game. This result is then extended to generalized Nash games, where we deduce two vector optimization problems providing necessary and sufficient conditions, respectively, for generalized Nash equilibria. Finally, we show that all prior results hold for vector- valued games as well. Multiple numerical examples are given and demonstrate the computational advantages of finding the set of Nash equilibria via our proposed vector optimization formulation in these cases.
2019/20, 2018/19, 2017/18, 2016/17, 2015/16