整体实施永久经理期权模型的若干问题

发布时间：2018-03-17 06:26

本文选题：期望效用最大化　切入点：经理期权　出处：《苏州大学》2013年硕士论文　论文类型：学位论文

【摘要】：经理股票期权(executive stock options,以下简称ESOs),是公司作为酬金发给员工的以本公司股票为标的资产的一种看涨期权。自20世纪80年代以来,ESOs己在美国和欧洲其他国家得到了长足的发展。不管从会计角度还是管理控制角度考虑,核算公司发行ESOs的成本尤为重要。为了能合理给出ESOs的价值,需要理性预测经理人未来的实施策略。最近,Song LipingYu Wanghui(见参考文献[8]),从经理人的期望效用最大化角度来研究整体实施永久ESOs的价值和经理人的实施策略。整体实施是指经理人在任意可实施时刻,要么不实施其持有的ESOs,要么一次性全部实施其持有的ESOs。在他们的模型中,经理人的期望效用最大值是一个最优停时问题的值函数,该值函数对应于一个退化抛物型变分不等式初值问题的解。他们证明了该变分不等式初值问题解的存在性、正则性以及自由边界的连续性和单调性,并在适当的条件下证明了解的唯一性。但他们没有证明所得到的变分不等式初值问题解的确对应于经理人的期望效用最大值,而本文的目的正是要解决这一问题。本文首先严格证明了：文献[8]中的期望效用最大化模型的价值函数,对应于[8]中所研究的退化抛物型变分不等式初值问题的粘性解。然后证明了文献[8]中所得到的解也是粘性解。最后证明了粘性解的唯一性。这样,本文就证明了[8]中所得到的解确实是经理人的期望效用最大值,同时还证明了该变分不等式初值问题的解是唯一的。
[Abstract]:Executive Stock Option (executive stock options, hereinafter referred to as ESOs), is the company as a call option on shares of the company for the underlying assets of the remuneration to employees. Since 1980s, ESOs has got a great development in the United States and other European countries. Not considering or control from the angle of view of accounting, accounting the company issued the cost of ESOs is very important. In order to give a reasonable ESOs value, need to implement strategies for future managers. Rational prediction
Recently, Song LipingYu Wanghui (see Ref. [8]), the implementation strategy for the overall implementation of the permanent ESOs value maximizing managers and managers from the expected utility angle. The overall implementation refers to the managers can be implemented at any time, either in the implementation of its holdings of ESOs, either a one-time implementation of all its holdings in their ESOs. in the model, the manager's expected utility maximum value is the value function of an optimal stopping problem, the value function corresponding to a degenerate parabolic variational inequality solution of initial value problems. They proved that the initial value of the variational inequality problem, continuity and monotonicity and regularity of the free boundary only, and under appropriate conditions, we prove the. But they did not prove that the obtained variational inequality solution to initial value problem of maximum expected utility indeed corresponds to the managers, and the purpose of this article It is just to solve this problem.
This paper is strictly proved that the value function of expected utility maximization model in literature [8], corresponding to [8] in the study of variational inequalities of initial value problem for Degenerate Parabolic viscosity solutions. Then it is proved that the solution obtained in Ref. [8] is the viscosity solution. Finally, we prove the uniqueness of the viscosity solution. So, this paper it proved that [8] in solution is indeed the maximum expected utility managers, but also proved that the variational inequalities for the solution of initial value problem is unique.

【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

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