Mathematical analysis and numerical methods for a PDE model of a stock loan pricing problem
Mathematical analysis and numerical methods for a PDE model of a stock loan pricing problem
复制标题
DOI：
10.1016/j.jmaa.2013.02.007
复制
发表时间：
2013-07
影响因子：
1.3
通讯作者：
A. Pascucci;M. Suárez-Taboada;C. Vázquez
中科院分区：
文献类型：
--
作者：
A. Pascucci;M. Suárez-Taboada;C. Vázquez
本文对一个股票借贷合同定价模型进行了数学分析，该模型考虑了贷款人在赎回时向借款人归还股票的累计股息收益率。更准确地说，该模型制定的障碍问题与Kolmogorov方程和多项式增长的解决方案的集合中的存在性和唯一性。并分析了解的一些正则性。接下来，对于该问题的数值解的组合的Crank-Nicolson拉格朗日-伽辽金增广拉格朗日有效集方法进行了说明。最后，一些数值例子说明了理论性质的最佳赎回边界以前在文献中所述。
In this paper the mathematical analysis of a model for pricing stock loan contracts, when the accumulative dividend yield associated to the stock is returned by the lender to the borrower on redemption, is carried out. More precisely, the model is formulated in terms of an obstacle problem associated to a Kolmogorov equation and the existence and uniqueness in the set of solutions with polynomial growth are obtained. Also some regularity properties of the solution are analyzed. Next, for the numerical solution of the problem the combination of Crank–Nicolson Lagrange–Galerkin with the augmented Lagrangian active set method is described. Finally, some numerical examples illustrate the theoretical properties of the optimal redeeming boundary previously stated in the literature.