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: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508535
• 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.

在数学上对财务变量进行建模时，重要的是考虑导致可牵引解决方案的动态，同时捕获经验数据的定性特征。 提出的研究计划涉及对各种随机方程，它们的特性以及它们在金融中建模的应用。特别是，我们将重点关注各种定期结构衍生品，商品合同，违约（信用）风险和保险产品的定价和套期保值。 还应注意有效实施模型所需的基础和分析工具。 要考虑的随机方程的主要类别是前向后的随机微分方程（简称FBSDE）。 FBSDE是一个随机方程式的耦合系统，其某些组件从初始条件和其他组件从随机终端条件从最初的条件开始向后发展。 文献中的几个问题已经通过以FBSDE来表征财务模型来解决。