Computational and statistical topics from modern finance

现代金融工具设计为股票、货币利率和其他证券的或有债权，在全球金融市场上取得了巨大的成功。它们为机构投资者提供了新的工具，以满足其多样化的金融需求。这些工具的成功在很大程度上可以归功于数学模型，这些模型为它们的定价提供了基础。在拟议的研究中，我将讨论与此类产品的风险管理相关的一些计算和统计问题。特别是，我将考虑对不同风险因素提供比现有模型更现实的描述的模型。它们基于JUMP和LEVY过程，并且通常仅通过变换来表征。这使得基于似然函数的经典方法变得不可行。我将集中讨论动态投资组合选择和美式合约定价的问题，这些问题取决于几种资产。我将研究的统计问题包括对涉及JUMP和Levy过程的模型的估计和过滤。

Modern financial instruments designed as contingent claims on equities, currency rates, and other securities have achieved enormous success in global financial markets. They have provided institutional investors with new vehicles to meet their diverse financial needs. The success of these instruments can largely be attributed to mathematical models that have given foundations for their pricing. In the proposed research, I will address some computational and statistical issues related to risk management of such products. In particular, I will consider models that provide more realistic descriptions of different risk factors than the existing ones. They are based on jump and Levy processes, and often are characterized by means of a transformation only. This makes classical methods based on likelihood functions infeasible. I will focus on the problems of dynamic portfolio selection and the pricing of American style contracts contingent on several assets. The statistical issues that I will study include estimation and filtering for models involving jump and Levy processes.