STABILITY OF TRAVELING WAVE SOLUTIONS IN A CREDIT RATING MIGRATION FREE BOUNDARY PROBLEM

Claude-Michel Brauner (1) , Yuchao Dong (2) , Jin Liang (2) , Luca Lorenzi (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 Tongji University
3 UNIPR - Università degli studi di Parma = University of Parma

In this paper, we study the stability of traveling wave solutions arising from a credit rating migration problem with a free boundary, After some transformations, we turn the Free Boundary Problem into a fully nonlinear parabolic problem on a fixed domain and establish a rigorous stability analysis of the equilibrium in an exponentially weighted function space. It implies the convergence of the discounted value of bonds that stands as an attenuated traveling wave solution.

Mots clés: 2020 Mathematics Subject Classification. Primary: 35R35; 35B25 Secondary: 35C07; 91G20 Free boundary problems stability traveling waves fully nonlinear parabolic problems credit rating migration; 35B25; Secondary: 35C07; 91G20 Free boundary problems; stability; traveling waves; fully nonlinear parabolic problems; credit rating migration

Domaines: Mathématiques [math]

Claude-Michel Brauner, Yuchao Dong, Jin Liang, Luca Lorenzi. STABILITY OF TRAVELING WAVE SOLUTIONS IN A CREDIT RATING MIGRATION FREE BOUNDARY PROBLEM. 2023. ⟨hal-04367574⟩