整体实施永久经理期权的定价问题  

The pricing problem of the perpetual executive stock options with block exercise

作　　者：宋丽平 SONG Li-ping(School of Mathematics and Finance,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

出　　处：《吉林师范大学学报（自然科学版）》2021年第4期52-56,共5页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11471175);福建省自然科学基金项目(2019J01807,2020J01907,2020J01909);教育部产学合作协同育人项目(201902030013);莆田市科技计划项目(2019RP001)。

摘　　要：在不完备市场情形下研究了整体实施永久经理期权的定价问题.首先,基于经理人的财富效用最大化法建立一个整体实施下永久经理期权定价的最优停时问题,给出相应的值函数;然后,基于效用无差别价格的定义,推导其与值函数之间的关系;最后,利用效用无差别价格与值函数的关系推导效用无差别价格的性质,包括单调性、上凸性、特殊效用函数下的线性性以及与标准的永久美式看涨期权价格的关系.借此希望相关结果能够为公司核算其发行经理期权的成本提供一定的参考价值.The pricing problem of the perpetual executive options with block exercise was investigated in incomplete market.Firstly,based on the executive s wealth utility maximization method,an optimal stopping time problem for pricing perpetual executive options was established,and the corresponding value function was given;Secondly,the relationship between utility indifference price and value function was deduced based on the definition of utility indifference price;Finally,the relationship between utility indifference price and value function was applied to deduce the properties of utility indifference price,including monotonicity,convexity,linearity under special utility function and the relationship between utility indifference price and standard permanent American call options price.It is hoped that the related results can provide some reference value for companies to calculate the cost of issuing executive stock options.

关 键 词：整体实施 效用函数 经理期权 效用无差别价格 性质 

分 类 号：O211.6[理学—概率论与数理统计] F830.9[理学—数学]