Iterative scheme for an elliptic non-local free boundary problem

Abstract

In this paper we treat a non-local free boundary problem arising in financial bubbles, where the model is set in the framework of viscosity solutions. We suggest an iterative scheme which consists of a sequence of obstacle problems at each step to be solved, that in turn gives the next obstacle function in the iteration scheme. The suggested approach gives a solution to the theoretical problem and paves the way for the numerical implementation, as done in the text below.