可转换公司债券定价中一类方程边值问题的求解  

Solving the Boundary Value Problem of a Class of Equations in the Pricing of Convertible Corporate Bonds

作　　者：宋丽平 姚旺进 林建伟 潘素娟 SONG Liping;YAO Wangjin;LIN Jianwei;PAN Sujuan(School of Mathematics and Finance,Putian University,Putian Fujian 351100,China;Key Laboratory of Financial Mathematics in Colleges and Universities of Fujian Province,Putian Fujian 351100,China;Department of Information Engineering,Fujian Commercial College,Fuzhou Fujian 350012,China)

机构地区：[1]莆田学院数学与金融学院,福建莆田351100 [2]金融数学福建省高校重点实验室,福建莆田351100 [3]福建商学院信息工程学院,福建福州350012

出　　处：《莆田学院学报》2022年第2期34-39,共6页Journal of putian University

基　　金：国家自然科学基金资助项目(11471175);福建省自然科学基金资助项目(2019J01807,2020J01907,2020J01909,2021J011102);教育部产学合作协同育人资助项目(201902030013)。

摘　　要：为研究一类永久可转换公司债券的定价问题,主要探讨一类二阶变系数退化的常微分方程的边值问题的两种求解方法。其一,通过变量代换将该边值问题转化为一个二阶常系数齐次线性方程,进而求出该边值问题的解;其二,通过幂级数解法并利用两个引理求出边值问题的解。此类边值问题的这两种求解方法可为可转换公司债券的合理定价提供理论基础。In order to study the pricing problem of a class of perpetual convertible corporate bonds,this paper mainly discusses two methods to solve the boundary value problem of a class of second-order degenerate ordinary differential equations with variable coefficients.Firstly,the boundary value problem is transformed into a second-order linear homogeneous equation with constant coefficients by the method of variable transformation,and then the solution of the boundary value problem is obtained.Secondly,the solution of the boundary value problem is obtained by power series solution and two lemmas.These two methods can provide a theoretical basis for the reasonable pricing of convertible corporate bonds.

关 键 词：可转换公司债券 定价 二阶常微分方程 边值问题 变量代换法 幂级数解法 

分 类 号：O175.1[理学—数学]