# American Institute of Mathematical Sciences

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## A free boundary problem for defaultable corporate bond with credit rating migration risk and its asymptotic behavior

 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 3 Department of Applied Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA

* Corresponding author: Jin Liang

Received  August 2018 Published  September 2019

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

In this paper, valuation of a defaultable corporate bond with credit rating migration risk is considered under the structure framework by using a free boundary model. The existence, uniqueness and regularity of the solution are obtained. Furthermore, we analyze the solution's asymptotic behavior and prove that the solution is convergent to an closed form solution. In addition, numerical examples are also shown.

Citation: Yuan Wu, Jin Liang, Bei Hu. A free boundary problem for defaultable corporate bond with credit rating migration risk and its asymptotic behavior. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2019207
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value function $\psi(x, t)$
free boundary
asymptotic behavior

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