On some non-linear boundary value problems related to a Black--Scholes model with transaction costs

2013/04/05 by Rubén Figueroa, Figueroa, Rubén, Maria do Rosário Grossinho +1
Economics, Econometrics and Finance · Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stochastic processes and financial applications #math.CA

paper · pdf · doi:10.48550/arxiv.1304.1690

openalex publication_date 2013/04/05 · arxiv created 2015/06/05 · arxiv updated 2015/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We deal with some generalizations on a Black--Scholes model arising in financial mathematics. As novelty in this paper, we consider a variable volatility and abstract functional boundary conditions, which allow us to treat a very large class of problems involving Black--Scholes equation. Our main results involve the existence of extremal solutions in presence of lower and upper solutions. Some examples of application are provided too.

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