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

Boundary value problems

Rubn Figueroa¹  Maria do Rosrio Grossinho² 

[1] Department of Mathematical Analysis, University of Santiago de Compostela, Santiago de Compostela, Spain;Department of Mathematics, CEMAPRE - ISEG, University of Lisboa, Lisboa, Portugal

关键词: Black-Scholes equation;    functional conditions;    discontinuous ODE’s;   

DOI  :  10.1186/s13661-015-0410-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We deal with some generalizations on a Black-Scholes model arising in financial mathematics. As a 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 applications are provided too.

【 授权许可】

CC BY