Numerical treatment to a non-local parabolic free boundary problem arising in financial bubbles
This work provides a numerical method for a specific free boundary problem in financial mathematics, but the problem is niche and the contribution is incremental.
The authors propose an iterative algorithm for a non-local parabolic free boundary problem in financial bubbles, proving convergence of the algorithm and its finite difference scheme, and present computational results.
In this paper we continue to study a non-local free boundary problem arising in financial bubbles. We focus on the parabolic counterpart of the bubble problem and suggest an iterative algorithm which consists of a sequence of parabolic obstacle problems at each step to be solved, that in turn gives the next obstacle function in the iteration. The convergence of the proposed algorithm is proved. Moreover, we consider the finite difference scheme for this algorithm and obtain its convergence. At the end of the paper we present and discuss computational results.