分期付款购房模型及其抛物障碍问题  

The Obstacle Problem for the Pricing of the Fixed Rate Mortgages

作　　者：坚雄飞[1] 易法槐[1] 

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《数学物理学报（A辑）》2007年第6期987-995,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(10671075);广东省自然科学基金(5005930);高等学校博士学科点专项基金(20060574002)资助

摘　　要：考虑常数利率条件下的分期付款购房模型,若风险资产市场价格服从几何布朗运动,则合约可以运用美式期权定价方法给出合理的价格.该文给出了分期付款购房合约定价的偏微分方程方法,得到一个一维抛物障碍问题,同时给出了贷款合约价格函数所联系的自由边界,并讨论了自由边界的单调性与有界性.The authors consider the mortgages with the constant market enviroment and the constant contract rate. Suppose that the asset price moved as a geometric Brownian motion, an one-dimensional parabolic variational inequality which arises from the fixed mortgages is studied, the existence and uniquencess of the solution are obtained. Moreover, the monotonicity and the regularity of the free boundary are proved as well.

关 键 词：期权定价 分期付款购房 抛物障碍问题 自由边界. 

分 类 号：O175.2[理学—数学]