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

  • * Corresponding author: Jin Liang

    * Corresponding author: Jin Liang 

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

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  • 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.

    Mathematics Subject Classification: Primary: 35R35, 35K10; Secondary: 35Q91.


    \begin{equation} \\ \end{equation}
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  • Figure 1.  value function $ \psi(x, t) $

    Figure 2.  free boundary

    Figure 3.  asymptotic behavior

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