论文标题
黑孔方程移动边界问题的解决方案的一般特性
General properties of the Solutions to Moving Boundary Problems for Black-Sholes Equations
论文作者
论文摘要
我们研究了一般特性，例如黑 - choles方程的移动边界值问题的解决方案表示，其最小最大估计，下梯度估计值和上层梯度估计以及有关溶液的空间变量的严格单调性。这些结果用于研究具有信用风险的定价固定债券的结构模型。我们首先证明了黑色 - choles方程的特殊固定边界值问题的解表示，最小值估计值，下梯度估计值和上层梯度估计以及有关溶液的空间变量的严格单调性。然后，将这些结果应用于以指数函数的形式，最小值估计值，下部和上部梯度估计值以及严格的单调性在解决方案的空间变量上，以指数函数的形式，最小值估计值，下部和上部梯度估计以及严格的单调性。最后，我们说明了如何将这些结果用于分析定价公式的推导以及具有信用风险的可固定债券的价格功能的财务分析（公司债券的提前赎回日期）。我们的结果可用于对具有信用风险的更一般可推杆债券的单因素结构模型的分析定价公式的推导和分析（公司债券具有早期赎回日期）。
We study general properties such as the solution representation of a moving boundary value problem of the Black-Scholes equation, its min-max estimation, lower and upper gradient estimates, and strict monotonicity with respect to the spatial variables of the solution. These results are used in the study of a structural model of pricing puttable bond with credit risk. We first prove the solution representation of a special fixed boundary value problem of the Black-Scholes equation, the min-max estimate, the lower and upper gradient estimates, and the strict monotonicity with respect to the spatial variables of the solution. Then, these results are applied to give the solution representation of a moving boundary value problem of the Black-Scholes equation with moving boundary in the form of an exponential function, the min-max estimate, the lower and upper gradient estimates, and the strict monotonicity results on the spatial variables of the solution. Finally, we illustrate how these results can be used in the derivation of analytical pricing formulae and financial analysis of price functions of puttable bonds with credit risk (corporate bonds with one early redemption date). Our results can be used for the derivation and analysis of the analytical pricing formulae of the one-factor structural model of a more general puttable bonds with credit risk (corporate bond with several early redemption dates).
