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# CWI develops new mathematical tools for analysis of rare events

PhD student Bohan Chen of CWI’s Stochastics group, developed new mathematical tools for rare event analysis. Chen’s PhD research has mainly focused on large deviations theory and rare-event simulation in heavy-tailed settings.

Publication date
6 Dec 2019

Rare events such as financial crises, floods, and power outages have a major societal impact. Obtaining insight into rare events is challenging, as it is hard to obtain data about such events from real-life measurements and/or large scale simulation studies. This makes rare event analysis a research area where mathematical techniques remain the primary method of choice to gain insights. For some types of rare events -like those caused by a single big shock- suitable techniques are not available yet, however.

In his thesis entitled 'Heavy tails: asymptotics, algorithms, applications', PhD student Bohan Chen of CWI’s Stochastics research group, developed new mathematical tools for rare event analysis. Chen’s research has been mainly focusing on large deviations theory and rare-event simulation in heavy-tailed settings. (Heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: they have heavier tails than the exponential distribution.)

Many rare events are caused by a single big shock, or ‘black swan’. Intuitively, heavy tails occur in systems whose behavior mainly is determined by large values that occasionally shock the system.  If you encounter a group of people that is a billionaire on average for example, it is quite likely that Bill Gates (or someone similar) is part of the group, and the wealth of the other people is negligible. In such a case, a good statistical distribution for incomes is the power law, also known as the Pareto distribution. Such distributions also appear in financial losses, file size on the internet, claim sizes in insurance, and blackout sizes in the power grid. A systematic mathematical theory has been lacking however, and no widely applicable efficient simulation techniques existed.

In this context, the thesis of Bohan Chen makes several major contributions to this lack of mathematical theory, by developing tools that can be used to analyze stochastic systems with power law behavior. In particular, Chen developed the first generic efficient rare event simulation algorithm that is applicable to a wide range of models. This has been illustrated in detail on a host of applications from queueing networks, mathematical finance, and insurance problems. A major technical contribution of Chen, has been the extension of recent results on rare events in sample paths of stochastic processes. In particular, Chen shows how to analyze rare events if such processes have a complicated dependence structure.

Chen’s work so far has been published in top-tier international journals such as Advances in Applied Probability and Mathematics of Operations Research. Currently, Chen is utilizing his expertise on rare events in at Munich Re, one of the very few global companies that insure insurance companies.