Final Report Summary - FIRM (Mathematical Methods for Financial Risk Management) The main of this project is to better understand the mathematical tools used in financial risk management. In particular, the 2009 financial crisis made it very clear the importance of frictions such as liquidity, the counter-party risk, etc. Given this goal, we incorporated financial frictions into risk measures that were developed earlier without these frictions. In technical terms, these frictions are transactions costs that can also be seen as illiquidity, other sources of illiquidity, random environment and also model uncertainty. These problems and questions are being intensively studied both in mathematical and also in economical, financial research communities. An example is the discussion of Tobin's tax or transaction tax, which proposes to charge a very small percentage for every transaction. Clearly this will have the possibly positive effect of reducing the transaction volume. However, it may also have the adverse consequences as it forces the market to deviate from the optimality. Our analysis of small transaction costs provides the appropriate tools to calculate the important quantities such the welfare impact of this tax. Another example is the desire to better understand model uncertainty and develop robust techniques to evaluate it and operate in such an environment. Robust techniques are already an important topic in economics, as outlined in the recent book "Robustness” by two Nobel price-winning economists, Hansen and Sergeant. Mathematically, they bring in very interesting questions which we have successfully analyzed.In summary, we have developed new and novel mathematical techniques to analyze the impact of these market frictions in the context of risk management. Several influential research results have been obtained. These results, obtained by the generous support of ERC, will continue with increasing intensity to develop and shape the general area of financial mathematics. Equally importantly, many young researchers have been trained on these important problems. They have then continued their work in leading academic institutions as well as in influential financial companies.
