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Free boundaries of credit rating migration in switching macro regions

  • * 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, 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.

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


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  • Figure 1.  Value function in different regimes

    Figure 2.  Free boundary

    Figure 3.  Differences between two cases

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