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 in room 32L.LG.03 (32 Lincoln's Inn Fields, LSE), 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.
IMPORTANT - Due to the ongoing COVID-19 epidemic all seminars have been cancelled until further notice.
Previous seminars in the series:
Thursday 12 March - Eduardo Ebi Jaber
Reconciling rough volatility with jumps
Starting from hyper-rough Volterra Heston models, for which we provide new existence uniqueness and stability results for any Hurst index in (-1/2,1/2], we construct a Markovian approximating class of one dimensional Heston-type models parametrized by a fast mean reversion speed and an unconstrained Hurst index. This class does not only enjoy closed form solutions for its Fourier-Laplace transform but is also able to mimick hyper-rough implied-volatility surfaces for any Hurst index in (-1/2,1/2]. More remarkably, for H smaller -1/2, sending the mean reversion to infinity, we obtain convergence of the reversionary model towards Lévy processes such as the IG-NIG.
Joint work with Ryan McCrickerd.
Thursday 27 February - Andreas Sojmark (Imperial College)
Dynamic default contagion: From Eisenberg--Noe to the Mean-field
In this talk, we will start by constructing a simple dynamic network model for interbank default contagion in the vein of the seminal clearing payment frameworks of Eisenberg & Noe (2001) and Rogers & Veraart (2013). The key feature, and main novelty, is a combination of stochastic dynamics for the banks’ external assets together with a realistic balance sheet methodology for determining early defaults (on interbank obligations). This then leads to the study of random default contagion events in continuous time. After first developing the model for a finite number of banks, we display a law of large numbers effect, which allow us to pass to the mean field limit of the interbank model. Thus, we can study default contagion via a conditional McKean–Vlasov type problem that respects the original network topology.
Thursday 13 February - Soren Christensen (CAU)
Nonparametric learning in stochastic control - exploration vs. exploitation
One of the fundamental assumptions in stochastic control of continuous time processes is that the dynamics of the underlying (diffusion) process is known. This is, however, usually obviously not fulfilled in practice. On the other hand, over the last decades, a rich theory for nonparametric estimation of the drift (and volatility) for continuous time processes has been developed. The aim of this talk is to make a first (small) step to bringing together techniques from stochastic control with methods from statistics for stochastic processes to find a way to both learn the dynamics of the underlying process and control good at the same time. To this end, we study a toy example motivated from optimal harvesting, mathematically described as an impulse control problem. One of the problems that immediately arises is an Exploration vs. Exploitation behavior as is well known in Machine Learning. We propose a way to deal with this issue and analyse the proposed strategy asymptotically.
2019/20, 2018/19, 2017/18, 2016/17, 2015/16