Probability in Finance and Insurance

The beauty of Statistics is that if you can take a large enough group of people, you can predict really well what the outcome will be overall

Our research works across the fields of probability, financial mathematics, and actuarial science on fundamental and real-world problems. Two of the most fascinating issues that are ubiquitous in virtually every aspect of our lives are how to predict the outcome of a future event in which uncertainty plays a role, and the understanding of the process of decision making under uncertainty. This calls for the construction of realistic yet tractable models to capture the impact of specific externalities and people's heterogeneity. A fruitful place where uncertainty arises are financial systems and financial markets, where an additional challenge is the so-called systemic risk, i.e., the threat that developments in the financial system can cause a seizing-up or breakdown of this system and trigger massive damages to the real economy. Last, but not least, both statistical and machine learning models for time-series play a crucial role when dealing with uncertainty.

Our research focuses on both the theoretical and applied aspects in the broad area of probability, financial mathematics, and actuarial science.

Specifically, we propose theoretical and computational models (aka algorithms) for describing and simulating a variety of situations in which uncertainty plays a role. A special focus is devoted to: (a) the understanding of the process of decision making under model uncertainty, with a particular attention to the impact of the chosen framework on the decision itself; (b) optimal stopping problems and optimal prediction problems; (c) the understanding of the imperfections in financial markets; (d) the pricing of financial and insurance contracts; (e) the understanding of ‘systemic risk’ in large financial system; (f) the development of Bayesian nonparametric and semiparametric frameworks for the description of time series models for financial data; (g) mean-field (games) models; (h) the development of statistical and machine learning models for the description of time series dynamics for financial data.

Andreas’ main research areas include weak convergence theory, interacting particle systems, mean-field problems, dynamic contagion modeling, and the analysis of systemic risk in financial markets.

Angelos’ main research areas include applications of probability and stochastic processes in finance and insurance, the development of procedures for stochastic simulations, inference for cluster processes and integer time series, and nonparametric statistics.

David's main research areas include stochastic portfolio theory, robust methods in finance, portfolio selection and optimization under various types of market frictions, rank-based modelling and stochastic control.

Erik’s main research areas include applications of Lévy processes in financial and insurance mathematics in particular, such as in optimal stopping, optimal control, and optimal prediction problems.

Gelly's main research areas include Bayesian nonparametric and semiparametric framework for financial modeling and forecasting, and the construction of quantile time series models for financial data.

Giulia's main research areas include high-frequency financial econometrics, mean-field games problems, dynamical systems, and stochastic analysis for the modeling of financial markets and machine learning.

Kostas' main research areas include arbitrage theory, the 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.

Pauline's main research areas include the understanding of the process of decision making under model uncertainty, risk measurement and product design, environmental economics and probability theory.

Umut's main research areas include the understanding of the imperfections in financial markets, equilibrium analysis in Market Microstructure Theory, inverse problem in Markov process theory, stochastic PDE and theory of enlargement of filtrations.

Theoretical and computational models that we study have applications in a variety of domains. We work on such applications in collaboration with various academic and industrial partners, for example in the areas of risk pricing and machine learning.

Andreas works on understanding how classical financial models can be revised to account for the looming risk of financial crises, big and small. Relatedly, he is looking at sound ways of quantifying the extent to which the financial markets are currently worrying about the risk of future crises.

Angelos' algorithms on stochastic simulation are used for the solution of problems in finance, operations research, and elsewhere. There are also applications in Bayesian statistics. His work with Wicher Bergsma in non-parametric statistics (test for independence) has given rise to research problems in computing science. His more recent work on estimation of cluster processes and integer time series has applications in general insurance.

David works on high-dimensional portfolio selection problems, particularly focusing on performance guarantees under model uncertainty and in the presence of market frictions. He uses a combination of theoretical models, modern numerical methods and empirical data analysis in his research.

Erik works on problems linked to predicting random times which appear in areas such as ruin theory and finance e.g. American options.

Gelly works on time series models which are useful for the estimation and forecasting of asset returns with the aim to understand the risk of financial decisions (for example, through measures such as Value at Risk (VaR) or expected shortfall).

Giulia has mostly engaged with financial econometrics and machine learning applications, working on time series consisting of high-frequency financial transactions.

Kostas has worked closely with practitioners working in asset management and portfolio selection, as well as risk management.

Pauline has always been very interested in bridging gaps, between the industry and the academia, between different fields. Her book The handbook of Insurance-Linked Securities presents the state of the art in Insurance-Linked Securitization, by exploring the various roles for the different parties involved in the transactions, the motivation for the transaction sponsors, the potential inherent pitfalls, the latest developments and transaction structures and the key challenges faced by the market. Her more recent book “Dialogues around Models and Uncertainty” aims at bridging the gap between different expertises and practices, by helping to develop a better understanding of how researchers from different scientific backgrounds view models and uncertainty. It provides key steps in fostering and encouraging interdisciplinary research.

Umut works on market microstructure for answering questions related to market design and regulations. In particular he wants to construct a realistic yet tractable equilibrium model that captures the impacts of specific trading mechanism and the heterogeneity of traders.

David Itkin. Martin Larsson. . Ann. Appl. Probab. 34 (3) 2940 - 2985, June 2024.

Brokmann, Xavier and Itkin, David and Muhle-Karbe, Johannes and Schmidt, Peter. (September 26, 2023).

Baurdoux, Erik J., Palmowski, Z and Pistorius, Martijn R. (2017). . Stochastic Processes and Their Applications.127, (8) pp. 2679-2698. ISSN 0304-149.

Baurdoux, Erik J., and Pedraza, JM. Lp optimal prediction of the last zero of a spectrally negative Lévy process (forthcoming in Annals of Applied Probability )

Dassios, Angelos and Chen, Zezhun. (2022). Stochastic Process and Their Applications, , May 2022, pages 456-480.

Dassios, Angelos, Qu, Yan and Zhao, Hongbiao (2021). . , , . Article No.19, pp 1–21.

Dassios, Angelos and Zhang, Junyi (2021). . Electronic Journal of Probability, 26. ISSN 1083-6489.

Griffin, Jim E. and Mitrodima, Gelly (2020). . Journal of Business and Economic Statistics. ISSN 0735-0015.

Mitrodima, Gelly and Jaideep Oberoi (2024). Journal of the Royal Statistical Society: Series C. Applied Statistics, 73 (1). 1 - 27.

Campi, L., De Angelis, T., Ghio, M., Livieri, G., (2022). . Annals of Applied Probability. 32.5: 3674-3717.

Kolokolov, A., Livieri, G., Pirino, D., (2020). Statistical inference for price staleness. Journal of Econometrics. 218.1: 32-81.

Kardaras, Kostas and Robertson, Scott, (2021). Ergodic robust maximization of asymptotic growth. Annals of Applied Probability. 31(4): 1787-1819.

Kardaras, Kostas, . Forthcoming in Annals of Applied Probability.

Søjmark, Andreas and Feinstein, Zachary, (2021). . SIAM Journal on Financial Mathematics 12 (4), SC83-SC97.

Søjmark, Andreas and Feinstein, Z, (2023). Contagious McKean–Vlasov systems with heterogeneity. Forthcoming in Finance and Stochastics.

Çetin, U. and Danilova, A., (2021). . SIAM Journal on Control and Optimization, 59(5), pp.3973-3998.

Çetin, U. and Larsen, K., (2023). . Transactions of the American Mathematical Society, Series B, 10(13), pp.381-406.

Makariou, Despoina, Barrieu, Pauline and Chen, Yining (2021). A random forest based approach for predicting spreads in the primary catastrophe bond market. Insurance: Mathematics and Economics, 101. 140 - 162. ISSN 0167-6687.

Barrieu, Pauline and Scandolo, Giacomo (2014). Assessing financial model risk. European Journal of Operational Research, 242 (2). pp. 546-556. ISSN 0377-2217.

Barrieu, Pauline and El Karoui, Nicole (2013). Monotone stability of quadratic semimartingales with applications to general unbounded quadratic BSDEs. The Annals of Probability, Vol. 41, p. 1831-1853.

Barrieu, Pauline and Sinclair-Desgagne, Bernard (2006) . Management Science, 52 (8). pp. 1145-1154. ISSN 0025-1909.

Pauline Barrieu - Professor

Research interests: Model uncertainty, insurance-linked securitization, contract designing, microinsurance, weather derivatives, environmental economics.

Erik Baurdoux - Associate Professor

Research interests: optimal stopping problem, optimal prediction and control, Lévy processes.

Umut Cetin - Professor

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

Angelos Dassios - Professor

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

David Itkin - Assistant Professor

Research interests: Stochastic portfolio theory, price impact, robust finance, stochastic control.

Kostas Kardaras - Professor

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