Finite Element Method for Solution of Credit Rating Migration Problem Model

TL;DR

This paper introduces a finite element method to solve a credit rating migration problem modeled as a free boundary problem, addressing discontinuities and proving convergence and stability.

Contribution

It presents a novel finite element approach for free boundary problems in credit rating migration, ensuring optimal convergence and stability.

Findings

Method achieves optimal convergence rates.

Numerical results confirm theoretical stability.

Approach effectively handles discontinuities.

Abstract

In this paper, we propose a finite element method to study the problem ofcredit rating migration problem narrowed to a free boundary problem. Freeboundary indeed separates the high and low rating region for a firm andcauses some difficulties including discontinuity of second order derivative ofthe problem. Exploiting the weak formulation of the problem utilized in theGalerkin method, the discontinuity of second order derivative is averted. Inthis investigation we prove optimal convergence and stability of the proposedmethod. Numerical results illustrate how derived convergence results areconsistent into practice ones.