Computational and statistical topics from modern finance

现代金融的计算和统计主题

• 批准号: 194347-2007
• 负责人: Kolkiewicz, Adam
• 金额: $ 1.31万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=392464
• 关键词: Computational; statistical; topics; modern; finance

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.

现代金融工具被设计为对股票、汇率和其他证券的或有债权，在全球金融市场上取得了巨大成功。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归功于为其定价奠定基础的数学模型。在拟议的研究中，我将解决一些与此类产品的风险管理相关的计算和统计问题。特别是，我将考虑比现有模型更真实地描述不同风险因素的模型。它们基于跳跃和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不可行。 我将集中讨论动态投资组合选择的问题， 美式合约的定价取决于几种资产。我将研究的统计问题包括涉及跳跃和Levy过程的模型的估计和过滤。