Computational optimization in finance and beyond

我的研究将数值方法与先进的计算技术相结合，以开发有效和强大的金融风险建模工具。复杂的金融工具，如衍生工具合同，在资本市场中变得越来越重要。这些工具的准确定价和风险管理工具至关重要。它们使投资者能够利用市场机会，同时保护他们免受不必要的风险。我的研究将集中在开发新的金融创新的标准方法不能很容易地应用这样的工具。例如，对冲基金投资最近吸引了机构和个人投资者的极大兴趣。因此，对冲基金的风险分析和建模就显得尤为重要。然而，这是非常困难的几个原因：缺乏透明度，许多动态的交易策略，经理人采用，以及事实上，只有少量的数据可用于模拟一个复杂的关系影响回报。此外，根据交易市场期权价格对资产价格演变的适当模型进行稳健校准，对于准确定价和有效对冲外来衍生产品至关重要。我打算利用新颖的数学公式，并创造性地将联合收割机数值方法与先进的计算技术相结合，以解决其中的一些问题。我将研究适当的风险模型，并开发可靠和有效的工具，对冲基金的风险分析，这将是金融专业人士使用。此外，我的研究可能会导致发现新的数学模型和数值方法，这可能适用于金融，保险和资源管理等其他领域的类似问题。

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.