Free boundaries of credit rating migration in switching macro regions

Wu Yuan; Liang Jin

doi:10.3934/mcrf.2019038

Article Contents

2020, Volume 10, Issue 2: 257-274. Doi: 10.3934/mcrf.2019038

This issue Previous Article Boundary null-controllability of semi-discrete coupled parabolic systems in some multi-dimensional geometries Next Article On the exact controllability and the stabilization for the Benney-Luke equation

Free boundaries of credit rating migration in switching macro regions

Wu Yuan^1, and
Liang Jin^2, ,

1.
School of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, China
2.
School of Mathematical Science, Tongji University, Shanghai 200092, China

^* Corresponding author: Jin Liang
^* Corresponding author: Jin Liang

Received: August 31, 2018

Revised: February 28, 2019

Early access: August 2019

Published: April 2020

The second author is supported by National Natural Science Foundation of China (No. 11671301)

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Abstract

In this paper, under the structure framework, a valuation model for a corporate bond with credit rating migration risk and in macro regime switch is established. The model turns to a free boundary problem in a partial differential equation (PDE) system. By PDE techniques, the existence, uniqueness and regularity of the solution are obtained. Furthermore, numerical examples are also presented.

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Mathematics Subject Classification: Primary: 35R35, 35K40; Secondary: 35Q91.

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Figure 1. Value function in different regimes

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Figure 2. Free boundary

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Figure 3. Differences between two cases

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