百慕大可转债价值的停时表示  

The Stopping Time Representation for the Value of Bermudian Convertible Bonds

作　　者：宋丽平 林鸿熙 江良 SONG Li-ping;LIN Hong-xi;JIANG Liang(School of Mathematics and Finance,Putian University,Putian 351100,China;School of Business,Putian University,Putian 351100,China)

机构地区：[1]莆田学院数学与金融学院,福建莆田351100 [2]莆田学院商学院,福建莆田35110O

出　　处：《数学的实践与认识》2020年第21期46-50,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11471175,11001142);福建省自然科学基金(2015J05012,2019J01807,2019J01817);莆田市科技计划项目(2018RP4003,2019RP001);教育部产学合作协同育人项目(201902030013);福建省社会科学规划项目(FJ2019B097)

摘　　要：研究n期百慕大可转换公司债券(简称可转债)的定价问题,考虑股价的稀释效应,采用基于公司的定价模型.首先,由风险中性定价原理给出百慕大可转债的价值.其次,通过定义一列停时,给出百慕大可转债价值的另一等价表示,最后,利用数学归纳法以及条件数学期望的性质进行证明.将百慕大可转债的价值表示为一个停时问题,这是进一步研究美式可转债的基础.This paper is concerned with the pricing of n period Bermudian convertible corporate bonds(convertible bonds for short),and adopts a company-based pricing model considering the dilution effect of stock price.First,the value of Bermudian convertible bonds is given by use of risk-neutral pricing principle.Secondly,a stopping time sequence is defined to obtain an equivalent representation for the value of Bermudian convertible bonds.Finally,applying mathematical induction and the properties of conditional mathematical expectation,the equivalent expression is proved.The expression of the value of Bermuda convertible bonds as a stopping time problem is the basis for further study of American convertible bonds.

关 键 词：百慕大可转债定价 稀释效应 数学归纳法 停时 条件数学期望 

分 类 号：O211.67[理学—概率论与数理统计] F831.51[理学—数学]