论文标题
Delta Greek非线性黑色 - choles方程的粘度解决方案
Viscosity solution of a Delta Greek nonlinear Black-Scholes equation
论文作者
论文摘要
在本文中，考虑了涉及交易成本的一类非线性期权定价模型。价格$ v $的非线性抛物线方程的扩散系数被认为是该期权基础资产价格的线性函数和gamma grheek $ v_ v_ {xx} $。这项工作的主要目的是研究三角洲希腊人的管理PDE。使用消失的粘度法证明了粘度溶液的存在。通过在初始问题中添加一个小的扰动来使方程式正规化，构造了一系列近似解决方案$ u^{\ varepsilon} $的序列，然后应用弱极限的方法来证明序列与delta方程的粘度解的收敛。构建的近似问题显示出良好的规律性，允许使用有效且健壮的数值方法。
In this paper, a class of nonlinear option pricing models involving transaction costs is considered. The diffusion coefficient of the nonlinear parabolic equation for the price $V$ is assumed to be a linear function of the option's underlying asset price and the Gamma Greek $V_{xx}$. The main aim of this work is to study the governing PDE of the Delta Greek. The existence of viscosity solutions is proved using the vanishing viscosity method. Regularizing the equation by adding a small perturbation to the initial problem, a sequence of approximate solutions $u^{\varepsilon}$ is constructed and then the method of weak limits is applied to prove the convergence of the sequence to the viscosity solution of the Delta equation. The approximate problems constructed are shown to have good regularity, which allows the use of efficient and robust numerical methods.
