Stochastic dynamics in financial modeling

金融建模中的随机动力学

• 批准号: 341777-2010
• 负责人: Hyndman, Cody
• 金额: $ 0.87万
• 依托单位: Concordia University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=458573
• 关键词: Stochastic; dynamics; financial; modeling

In modeling financial variables mathematically it is important to consider dynamics which lead to tractable solutions while at the same time capture qualitative features of empirical data. The proposed research program involves the study of various stochastic equations, their properties, and their application to modeling in finance. In particular we shall focus on the pricing and hedging of various term-structure derivatives, commodity contracts, default (credit) risk, and insurance products. Attention shall also be given to the foundations and analytic tools necessary to implement the models effectively. The main class of stochastic equations to be considered are forward-backward stochastic differential equations (FBSDEs, for short). A FBSDE is a coupled system of stochastic equations of which certain components evolve forward in time from an initial condition and other components evolve backward in time from a random terminal condition. Several problems in the literature have been solved by characterizing financial models in terms of FBSDEs.

在对金融变量进行数学建模时，重要的是要考虑导致易于处理的解决方案的动态，同时捕获经验数据的定性特征。 拟议的研究计划涉及各种随机方程、其性质及其在金融建模中的应用的研究。我们将特别关注各种期限结构衍生品、商品合约、违约（信用）风险和保险产品的定价和对冲。 还应关注有效实施模型所需的基础和分析工具。 要考虑的主要一类随机方程是前向-后向随机微分方程（简称 FBSDE）。 FBSDE 是随机方程的耦合系统，其中某些分量从初始条件随时间向前演化，而其他分量从随机终端条件随时间向后演化。 文献中的几个问题已经通过用 FBSDE 描述金融模型来解决。