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Mathematical risk modeling

The recording and quantification of risks using mathematical models plays a major role in economics, but also in other scientific disciplines such as climatology or epidemiology. In the financial sector, for example, equity capital reserves are required, which are derived from quantitative risk measures within the framework of the Basel III regulations. In the insurance industry, risks for claims must be quantified and taken into account when calculating premiums, and equity reserves are determined on the basis of Solvency II. In economics, uncertainties and thus risks are quantified in the calculation and prediction of macro indicators such as unemployment rate, inflation or GDP and are included in policy advice. In climatology, the prediction of global warming together with the quantification of the resulting risks and consequences for the economy, society and the environment is an essential topic. Health risks and their economic and societal consequences have been highlighted in the Corona pandemic.

Mathematical challenges in risk modeling are, on the one hand, the construction of suitable quantitative risk measures that also take into account the global interconnectedness of today's world and, on the other hand, their estimation on the basis of observed data subject to uncertainties. This requires methods from all areas of applied mathematics, i.e. stochastics, optimization and numerics, and is also closely related to data science and uncertainty quantification.
Research at the department is supported by associate professorships in finance and actuarial mathematics.