A fully nonlinear problem arising in financial modelling
1 ISEG, CEMAPRE - Technical University of Lisbon, Rua do Quelhas 6, Lisboa, 1200-781, Portugal
2 Department of Mathematics, University of Trás-os-Montes e Alto Douro, Apartado 1013, Vila Real, 5001-801, Portugal
Boundary Value Problems 2013, 2013:146 doi:10.1186/1687-2770-2013-146Published: 13 June 2013
We state existence and localisation results for a fully nonlinear boundary value problem using the upper and lower solutions method. With this study we aim to contribute to a better understanding of some analytical features of a problem arising in financial modelling related to the introduction of transaction costs in the classical Black-Scholes model. Our result concerns stationary solutions which become interesting in finance when the time does not play a relevant role such as, for instance, in perpetual options.