Computational optimization in finance and beyond

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My research combines numerical methods with advanced computing technologies to develop efficient and robust tools for modeling financial risk. Complex financial instruments such as derivative contracts have become increasingly important in capital markets. Accurate pricing and risk management tools for these instruments are essential. They enable investors to take advantage of market opportunities while shielding them from undue risk. My research will focus on developing such tools for new financial innovations where standard methodologies cannot be readily applied. Hedge fund investments, for example, have recently attracted tremendous interest from institutional and individual investors. As a result, risk analysis and modeling of hedge funds are of crucial importance. However this is very difficult for several reasons: a lack of transparency, the many dynamic trading strategies that the managers employ, and the fact that only a small amount of data is available to model a complex relationship affecting returns. In addition, robust calibration of an appropriate model for asset price evolution from the traded market option prices is crucial for accurate pricing and effective hedging of exotic derivative products. I intend to utilize novel mathematical formulations and to creatively combine numerical methods with advanced computing technologies to solve some of these problems. I will investigate appropriate risk models and develop reliable and efficient tools for hedge fund risk analysis which will be of use for financial professionals. In addition, my investigation can potentially lead to discovery of new mathematical models and numerical methods, which can potentially be applicable to similar problems in other areas of finance, insurance, and resource management.