In this thesis, we study asymptotic behaviors of a free boundary arised from the evaluation of a corporate bond subject to changes of the credit rating of the underlying company. The credit rating migration is modeled by a free boundary which separates different credit rating regions in a state space. We first formulate the mathematical problem and then we establish the well-posedness of the problem and the long time-to-expiry behavior of the solution. As a result, we describe the location and asymptotic line of the free boundary. Certain numerical simulations are also provided.

中文翻译：

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具有信用评级迁移风险的公司债券评估提出的自由边界的渐近行为

在本论文中，我们研究了在标的公司信用评级发生变化的情况下对公司债券的评估所产生的自由边界的渐近行为。信用评级迁移由一个自由边界建模，该边界将一个状态空间中的不同信用评级区域分开。我们首先制定数学问题，然后建立问题的适定性和解决方案的长时间到期行为。因此，我们描述了自由边界的位置和渐近线。还提供了某些数值模拟。