The PDEs and Numerical Scheme for Derivatives under Uncertainty Volatility

Fan Yulian

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The PDEs and Numerical Scheme for Derivatives under Uncertainty Volatility

机译：不确定性波动下衍生物的PDE和数值方案

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We use the stochastic differential equations (SDE) driven by G-Brownian motion to describe the basic assets (such as stocks) price processes with volatility uncertainty. We give the estimation method of the SDE's parameters. Then, by the nonlinear Feynman-Kac formula, we get the partial differential equations satisfied by the derivatives. At last, we give a numerical scheme to solve the nonlinear partial differential equations.

机译：我们使用由G-Brownian Motion驱动的随机微分方程（SDE）来描述具有波动性不确定性的基本资产（如股票）价格流程。我们提供了SDE参数的估计方法。然后，通过非线性Feynman-Kac公式，我们得到了衍生物满足的部分微分方程。最后，我们提供了一种解决非线性偏微分方程的数值方案。

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《Mathematical Problems in Engineering》 |2019年第12期|1268301.1-1268301.7|共7页
作者
Fan Yulian;
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North China Univ Technol Dept Math Beijing Peoples R China;

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1. The PDEs and Numerical Scheme for Derivatives under Uncertainty Volatility [J] . Yulian Fan Mathematical Problems in Engineering: Theory, Methods and Applications . 2019,第1期

机译：不确定性波动下衍生物的PDE和数值方案
2. Calibration of local volatility model with stochastic interest rates by efficient numerical PDE methods [J] . Julien Hok, Shih-Hau Tan Decisions in economics and finance . 2019,第2期

机译：通过有效的数值PDE方法用随机利率校准局部波动率模型
3. The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models [J] . Nardini John T., Bortz D. M. Inverse Problems: An International Journal of Inverse Problems, Inverse Methods and Computerised Inversion of Data . 2019,第6期

机译：数值误差对平流PDE模型参数估计和不确定量化的影响
4. UNCERTAINTY ESTIMATION OF NUMERICALLY COMPUTED QUANTITIES: A CASE STUDY FOR THE TWOFOLD DERIVATIVE [C] . M. ORLT, D. RICHTER, P Ciarlini Workshop on Advanced Mathematical and Computational Tools in Metrology . 2000

机译：数值数量的不确定性估计：双重衍生物的案例研究
5. High order numerical schemes for PDEs and applications to CFD. [D] . Fu, Huankun. 2013

机译：PDE的高阶数值方案及其在CFD中的应用。
6. Development of a Rapid Mass Spectrometric Determination of AMP and Cyclic AMP for PDE3 Activity Study: Application and Computational Analysis for Evaluating the Effect of a Novel 2-oxo-12-dihydropyridine-3-carbonitrile Derivative as PDE-3 Inhibitor [O] . Ilaria Cicalini, Barbara De Filippis, Nicola Gambacorta, 2020

机译：用于PDE3活性研究的AMP和循环AMP的快速质谱测定方法的开发：用于评估新型2-氧-12-二氢吡啶-3-腈衍生物作为PDE-3抑制剂的作用的应用和计算分析
7. The PDEs and Numerical Scheme for Derivatives under Uncertainty Volatility [O] . Yulian Fan 2019

机译：不确定性波动下衍生物的PDE和数值方案

The PDEs and Numerical Scheme for Derivatives under Uncertainty Volatility

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