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Joint Risk & Stochastics and Financial Mathematics Seminar

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.

Upcoming speakers:

Thursday 21 October 2021 - Philippe Casgrain (ETH Zürich)
12:00 on Zoom - register here

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.

Previous seminars in the series:

Thursday 7 October 2021 - 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.

 

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