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February 2019

Mathematics of Risk

From observing previous and current financial and other problems it is clear that risk is a pervasive component of existence for all organizations. What is perhaps less well known is how mathematics can model exposure and indicate appropriate steps to reduce loss. Financial risk is only one aspect of the subject, though at the moment probably the most highly developed mathematically. Risk arises when companies plan future operations; risk arises when governments decide policies at the national or international level; indeed, risk arises when individuals make plans for the future. The essence of risk, indeed of life, is that the future is unknown. Here mathematics, the study of patterns, can contribute. Mathematically the future can be modelled by considering, in simplified frameworks, possible scenarios or future states of the world. These outcomes can then be assessed using methods from probability and random processes. Objectives of the research include: (1) the development of new risk measures, particularly those related to nonlinear expectations and backward stochastic differential equations, (2) their implementation in both financial and non financial settings, (3) the calibration or tuning of the models, (4) the combining of information from different sources, and (5) the application of the results to problems provided by industry and government. While financial risk has, so far, motivated the most sophisticated modelling, mathematics can contribute to assessing and mitigating the effects of risk in many situations.

Robert ElliottStochastic modelling, General theory of processes, Backward stochastic differential equations, Filtering, Systems engineering, Hidden Markov processes, Protein sequencing