Stochastic modelling in mathematical and computational finance

数学和计算金融中的随机建模

• 批准号: RGPIN-2015-04125
• 负责人: Hyndman, Cody
• 金额: $ 1.02万
• 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: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=654177
• 关键词: Stochastic; modelling; mathematical; computational; finance

Stochastic modelling in mathematical and computational finance is the focus of the proposed research program.  Mathematical and computational finance considers the uncertain future behaviour of financial or economic variables and systems; presents a theory for the valuation and risk management of derivative securities; and provides a quantitative framework for examining various investment, managerial, and regulatory decisions. Various probabilistic models, statistical estimation methods, and computational algorithms which are motivated by financial applications shall be considered.  Addressing applied problems in a realistic framework also drives new theoretical research and is the impetus for novel theoretical advances in probability and statistics.  The research integrates various aspects of mathematical and computational finance starting with the development of new stochastic models for fundamental financial and economic quantities such as interest rates and asset volatility. We shall develop new pricing and risk management theories methodologies that allow market participants to value and hedge financial derivatives exposed to credit risk.  We also plan to study the stochastic equations which characterize these new valuation and risk management methods, deriving explicit solutions where possible but  focusing on realistic modelling which requires the creation of new efficient computational algorithms for solving these equations.***The first objective of the proposed research program is the study of forward -backward stochastic differential equations (FBSDEs) and applications in mathematical finance. An FBSDE is a coupled system of stochastic equations with components that evolve forward in time from a specified initial condition and components that evolve backward in time from a random terminal condition.  We shall use FBSDEs to characterize a new pricing methodology for credit risk derivatives such as defaultable bonds and extend this method.  The second objective is the development of numerical methods for the solution of FBSDEs since the class of FBSDEs with explicit solutions is limited.  We shall further develop a new numerical method we created, based on the fast Fourier transform, to higher dimensions.  The third objective involves the study of problems in mathematical finance that can be characterized as producing or depending on large amounts of high- dimensional data. Our goal is to extend to financial contexts certain modelling and statistical techniques for high- dimensional data that effectively reduce the dimension to the point that an accurate lower dimensional model can be implemented.  Infinite dimensional models of forward interest rate processes shall be the first example considered so that, by reducing the dimension,  we can create new parsimonious financial models that preserve the key features of the theoretical model and the observed data.**

数学财务的随机建模是拟议的研究计划的重点。由财务应用激励的算法应促进新的理论研究，这是概率和统计学的新型理论的动力。经济量，诸如大比例的波动。他需要创建新的有效计算算法来解决这些方程式。随机终端条件。较高的尺寸。对数学金融的问题的研究概括为产生或贬低的数据远期利率过程的范围应为最终的示例，以便我们可以创建新的简约的财务模型，即理论模型模型模型模型模型和观察到的数据的关键特征**