2020/05/04 by Rui M.P. Almeida, Almeida, Rui M. P., Teófilo Domingos Chihaluca +3
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Applied mathematics #Black–Scholes model #Econometrics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Fractional Differential Equations Solutions #Mathematics #Nonlinear system #Physics #Stochastic processes and financial applications #Thermodynamics #Viscosity
paper · pdf · doi:10.48550/arxiv.2005.01358
openalex publication_date 2020/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Vxx. 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 uε 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.