Mathematical Challenges in Financial Risk Analysis

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My research project consists of the conception of various risks, the measurement, the analysis, and the management of financial risks under unexpected circumstances. Mathematical modeling, analyzing, computing (simulations) approaches are required to solve the exciting and challenging research problems proposed in the application. ******In the current generation of data-rich environment, high-frequency trading algorithms and advanced learning techniques in financial markets become important issues. As a relatively new phenomenon, much of the discussion is not backed by solid academic research. They operate and improve market quality in usual times, but may stop operating and thus cause the prices to disappear (or clearly unreasonable traded prices) in extreme circumstances. Market stability also relates to the issue of liquidity risk in financial markets. At the time of stress, the high-frequency trading stops providing liquidity and becomes the demander of liquidity, the provision of liquidity seriously deteriorates, which can cause substantial volatility. This is explained by the fact that market participants react to immediate information, in other words, that noise creates noise. ******Both the models and the people who use them are lacking the ability to articulate the risk of the underlying and that related to the actual market. Models become more sophisticated, but the same logic has persisted. Today, it is crucial to develop new tools (and train professionals) for risk analysis, by reworking on the determination of the exposure to risk. It is more important than ever to explore new research approaches for facing current challenges, and this proposal reflects a big part of this new trend.