Probability in finance and insurance

Model uncertainty, insurance-linked securitization, contract designing, microinsurance, weather derivatives, environmental economics

Pauline’s recent research has mainly (but not exclusively) focused on understanding the process of decision making under model uncertainty, with a particular attention to the impact of the chosen framework on the decision itself. Particular examples have included the impact of mortality models on the evaluation of longevity related products, or the development of some financial measures for regulatory capital requirements in a context of model uncertainty.

She has also worked in the area of risk measurement and product design, in particular insurance-linked securities, environmental economics and probability theory, especially Backward Stochastic Differential Equations. Pauline enjoys working with collaborators from different fields, background and experience, from academic or industry background, as this often challenges standard views and brings interesting and exciting perspectives.

Pauline was awarded the Bachelier Prize in 2018.

Optimal stopping problem, optimal prediction and control, Lévy processes

Erik Baurdoux's research focuses mainly on Lévy processes and their applications in financial and insurance mathematics in particular. Erik is particularly interested in optimal stopping and optimal prediction problems.

Erik obtained his PhD in 2007 from Utrecht University following research visits to Heriot-Watt University and the University of Bath.

Stochastic analysis, theory and applications of Markov processes, market microstructure, climate finance, Monte-Carlo simulation

Umut’s research falls into the field of stochastic analysis, often with an applied emphasis on understanding the imperfections in financial markets. More recently his research has movedtowards equilibrium analysis in Market Microstructure Theory, especially in the presence of asymmetric information. Analysis of such models leads to interesting inverse problems in Markov processes theory and one needs to apply a combination of various techniques from stochastic filtering, stochastic and partial differential equations, conditioning of Markov processes, and the theory of enlargement of filtrations.

Although there is a vast amount of works in the economics literature on market microstructure, they often lack the sufficient level of generality to be applied safely to today's highly complex financial markets. The necessity of having a more general and robust model becomes more paramount when one considers the fact that a good market microstructure model is the basis for answering questions related to market design and regulation.

However, such extensions have not so far been adequately dealt with in the literature due to the technical difficulties involved with equilibrium in a general framework. A typical challenge that arise in this field is the construction of realistic yet tractable equilibrium models that capture the impacts of specific trading mechanisms and the heterogeneity of traders. Umut’s recent research has extended the available theory in many ways by incorporating more general private signals, default risk and risk aversion.

Applied probability, stochastic process including inference, path dependent financial options, insurance mathematics, stochastic simulation and non-parametric methods

Angelos’ research is on applications of probability and stochastic processes in finance and insurance. He particularly likes problems that are on the interface of these two fields. Some examples of his research are work on exotic look back options, point processes with a strong element of contagion and insurance ruin based on these processes. Anything in these areas that can produce interesting or beautiful mathematics is something he would look at.

Angelos also uses and develops procedures stochastic simulation which is another area of interest. More recently he has developed an interest in the area of non-parametric statistics and in particular developing tests for independence. He enjoys supervising PhD students and there is a large number of past and current ones and is always looking for creative and enthusiastic new ones. He also enjoys collaborating with researchers from all over the world.

Stochastic portfolio theory, price impact, robust finance, stochastic control

David Itkin's research focuses on tackling problems in mathematical finance and stochastic analysis that are high-dimensional in nature. A main application in David's research is portfolio selection, where high dimensionality is inherent due to the large number of securities available for investment. His work has contributed to the understanding of open markets (i.e. markets where assets available for investment change over time), stochastic portfolio theory and robust finance under price stability.

More recently, David has also started working on portfolio construction in the presence of price impact. A selection of probabilistic tools employed in his work are reflected stochastic differential equations, ergodic theory, stochastic control and rank-based analysis.

David holds a PhD in Mathematics from Carnegie Mellon University. Prior to joining LSE, he was a Chapman Fellow at Imperial College London.

Stochastic analysis and semimartingale theory, mathematical finance and economics, convex analysis, stochastic control and optimization, Monte-Carlo simulation

Professor Kostas Kardaras' research is focused on the field of Stochastic Analysis and, in particular, on its applications in Financial Mathematics. He has worked and published on arbitrage theory, pricing of financial and insurance contracts, financial equilibrium, stochastic optimal control, robust long-term investment, informational asymmetry, game theory, Monte-Carlo simulation, as well as more abstract topics in semimartingale theory and functional analysis.

Prior to his position at the Statistics department of the LSE, Professor Kardaras worked as an Assistant professor in the Mathematics & Statistics department of Boston University.

High-frequency financial econometrics, statistical and machine learning models for time series, mean field games theory

Giulia was Assistant Professor at Scuola Normale Superiore (SNS) from February 2020 to November 2022. Previously she was a Post-doc researcher at SNS, where she obtained a Ph.D in Financial Mathematics in October 2017 with the score of 70/70 with laude. In 2013, Giulia did a post-graduate course in Mathematical Finance at the University of Bologna where she obtained a score of 30/30 with laude and an internship at Mediobanca a leading investment bank in Italy. Giulia graduated in 2012 in Mathematics at the University of Padova with the score of 100/100.

Giulia's research focuses mainly on financial econometrics and stochastic analysis for the modelling of financial markets (both at high and low frequency) and Mean-Field Game (MFG). She is currently developing machine learning techniques for the standard memory, forecasting, and filtered problems that appear the parametric stochastic time series context. Also, Giulia aims to provide mathematical foundation based on the theory of MFGs to implement Deep Neural Network (DNN) models.

Bayesian nonparametrics, quantile autoregression, stationarity, value-at-risk, expected shortfall

Gelly’s research interests lie in financial modelling and forecasting and her research uses among others Bayesian nonparametric and semiparametric framework, via Markov chain Monte Carlo, for the construction of quantile time series models for financial data. Prior to joining the Department of Statistics, Gelly spent four years at the University of Kent, where she completed a PhD in Actuarial Science at the School of Mathematics, Statistics, and Actuarial Science. Her PhD thesis was on the use of quantile methods to better estimate and forecast the time-varying conditional asset return.

Stochastic analysis, weak convergence theory, mean-field problems, contagion modelling, credit risk, systemic risk

Andreas Søjmark is part of the research group 'Probability in Insurance & Finance' in the stats department here at the LSE. Very briefly, Andreas works on problems at the interface of stochastic analysis and mathematical finance, focusing in particular on the mathematical challenges stemming from the need to understand 'systemic risk' in large financial systems. That is, the risk of financial distress spreading through the financial system and creating large scale problems akin to what we witnessed in the 2008-2009 global financial crisis and many other smaller crashes.

Before joining the LSE, Andreas held a Chapman Fellowship in Mathematics at Imperial College London, and before that he spent the summer of 2019 as an LMS Early Career Fellow at Columbia University in New York just after finishing his DPhil in Mathematics at the University of Oxford.