IJPAM: Volume 51, No. 4 (2009)

A NOTE ON A STATIONARY PROBLEM FOR
A BLACK-SCHOLES EQUATION WITH
TRANSACTION COSTS

M.R. Grossinho$^1$, E. Morais$^2$
$^1$Departamento de Matemática
Instituto Superior de Economia e Gestão - ISEG
Universidade Técnica de Lisboa
6, Rua do Quelhas, Lisboa, 1200-781, PORTUGAL
e-mail: mrg@iseg.utl.pt
$^2$Departamento de Matemática
Universidade de Trás-os-Montes e Alto Douro - UTAD
Apartado 1013, Vila Real, 5001-801, PORTUGAL
e-mail: emorais@utad.pt


Abstract.In this paper, we consider the nonlinear Black-Scholes equation arising in certain option pricing models with transaction costs. Following the classical Leland approach and applying Itô's Lemma, the stochastic model yields the nonlinear parabolic partial differential equation for the option price which is denoted by $V(S,t),$ Vt+12^2S^2^2V

Received: February 13, 2009

AMS Subject Classification: 35J25, 35J60

Key Words and Phrases: nonlinear Black-Scholes equation, transaction costs, stationary convex solutions, upper and lower solutions, existence and localization

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 4