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A fully nonlinear problem arising in financial modelling

Maria do Rosário Grossinho1* and Eva Morais12

Author Affiliations

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

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Boundary Value Problems 2013, 2013:146  doi:10.1186/1687-2770-2013-146

Published: 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.