Beatrice Acciaio's recent research has been manly focused on problems related to model-independent finance, such as robust pricing and hedging of derivative securities, pathwise super-replication and martingale inequalities, transport based approach to Skorokhod embedding, the effect of insider information in a financial market in a robust framework. In those cases, results are obtained by relying on the connection between different areas of mathematics, from optimal transportation to probability theory and stochastic analysis.

Another direction of Beatrice's research is concerned with model-uncertainty in mathematical finance. In several papers with different coauthors, Beatrice contributed to the study of preference modeling, determination of margin requirements, analysis of the optimal risk sharing problem.

Professor Pauline Barrieu Chair in Statistics

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Pauline Barrieu’s primary research interests are in several fields and their interface: first the interface between insurance and finance, as underlined by her work on optimal risk transfer and insurance-linked securitisation, then the measurement of risk, but also the understanding and quantification of the impact of model uncertainty on decision making, with various possible application areas including actuarial science, finance or environmental economics. She is especially interested in inter-disciplinary research.

Professor Barrieu is the co-editor with Luca Albertini of The Handbook of Insurance-Linked Securities, 2009, published by Wiley-Blackwell, London, UK. ISBN 978-0-470-74383-6.

Dr Erik Baurdoux Associate Professor

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The majority of Erik Baurdoux's current research involves applications of Lévy processes, which are processes with independent and stationary increments.These are widely used in financial and insurance mathematics. Erik studies various optimal stopping and stochastic control problems for Lévy processes and investigates the so called smooth-fit property, which plays an important role many applications such as inventory problem and American option pricing. Erik also studies the so called optimal prediction problems, where, for example, the time of the all-time supremum is to be predicted by a stopping time. For insurance applications, Erik applies Lévy processes to study the notion of Parisian ruin which allows an insurance company to survive for a period of time when its surplus becomes negative. Finally, Erik also investigates asset price drawdowns, which measure the distance of the current price away from its maximum attained to date.

Dr Luciano Campi Associate Professor

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Luciano Campi's research focuses on stochastic calculus and mathematical finance. More specifically, it has followed three distinct tracks in the last few years: the study of market frictions, for instance the problem of optimal investment for an investor facing proportional transaction fees; modelling energy and more generally commodity markets aiming at pricing and hedging of structured products; equilibrium models with different types of agents, among which an insider who knows more than the others and exploits his informational advantage to maximizes his/her expected profit. More recently, Luciano's research interests have turned to two new topics: applications of optimal transports to robust pricing and hedging, that is computing derivative prices and the corresponding hedging strategies so as to reduce the model risk; model of interactions such as stochastic games and, more precisely, mean field games where the rewards of each agent depend on his/her own strategy as well as the average behaviour of the other players. The latter turns out to be a very flexible setting for financial and economical applications.

Dr Umut Çetin Associate Professor

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Umut Çetin’s primary area of research is market microstructure theory. Typical challenges that arise in this field of study include, but are not limited to, constructing equilibrium models that capture realistically the impacts of specific trading mechanisms and heterogeneity of traders on price formation, coming up with measures for market liquidity, and measuring the sensitivity of liquidity and other indicators of market behaviour on different trading mechanisms or market parameters. As such, it has direct applications in market regulation and design. In particular, it proposes answers to policy questions such as “What are the benefits of introducing a financial transaction tax?” or “Is high frequency trading harmful?”

Analysis of above models leads to interesting inverse problems in Markov processes theory and one needs to apply various techniques from stochastic filtering, stochastic and partial differential equations, and the theory of enlargement of filtrations. In a series of joint works with multiple co-authors, Çetin has developed a theory for a certain type of conditioning for Markov Processes, which is essential in establishing the existence of equilibrium in a class of market microstructure models.

Çetin is also interested in pure and other applied problems in stochastic analysis, Markov process and martingales.

Dr Angelos Dassios Associate Professor

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Angelos Dassios' recent research is in three areas. One of them is on the pricing of path dependent options in financial mathematics. Two examples are quantile options and Parisian options. Another area is point processes and applications in insurance and credit risk. The most recent is the introduction of dynamic contagion models (here), a very large class of processes encompassing both Hawkes and Cox models. This work is at the interface of financial and insurance mathematics. Ruin theory problems are also part of this research. Finally, Angelos is working on the development of measures of association in non-parametric statistics. In particular tests for independence for two arbitrary random samples.

Professor Kostas Kardaras Chair in Statistics

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Kostas Kardaras' research is based on Stochastic Analysis and its applications to mathematical finance and economics. Topics include arbitrage and valuation theory (mostly in situations where market anomalies prevail); financial equilibrium (in both rational and behavioural settings); risk-sharing (and strategic behaviour of agents); asymmetric information; portfolio optimisation under investment constraints (notably, under draw-down constraints); computational methods; convex analysis on probability spaces.

Dr Hao Xing Associate Professor

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Hao Xing’s research mainly focuses on Stochastic Control and its applications to Mathematical Finance and Economics. More specifically, Hao studies interacting agents in financial markets, trying to understand how they collaborate or compete with each other, and how individual agent’s characteristics (such as preference and information) impacts macro-economic quantities, such as asset price and volatility. Hao also investigates optimal investment problems aiming to obtain semi-explicit optimal portfolio allocations in markets with stochastic investment opportunities. More recently, Hao is working on choosing trading strategies in markets with micro-structure noise and price impact, and designing optimal contracts between principal and agent, taking into account moral hazard and adverse selection. From the theoretical perspective, Hao Xing studies Backward Stochastic Differential Equations which provides theoretical framework for all above applications.