整体和非限制实施下永久经理期权的最优实施策略

发布时间：2018-05-28 11:48

本文选题：经理期权 + 整体实施　；参考：《苏州大学》2013年博士论文

【摘要】：经理期权简称为ESOs,是公司作为酬金发给经理或员工的一种美式看涨期权。自20世纪80年代中期以来,ESOs已成为美国和其他国家高管薪酬的重要组成部分。ESOs可看作为公司从经理或员工那里买到服务而支付的成本。由于ESOs的发行数量之多,其对应的公司发行成本也很可观。为了给出ESOs的合理价值,需要理性预测经理人未来的实施策略。由于公司高管是不能卖空公司股票的(非法的),因此经理人不能构造由公司股票、ESOs和无风险债券组成的组合来对冲ESOs的风险。事实上,这是一个不完全市场,这就使得无套利定价方法不能用来对ESOs进行定价。本文主要研究与金融市场上的永久ESOs的最优实施策略有关的一个抛物型变分不等式的定解问题。我们通过严格的数学分析,研究了相应解的存在性、唯一性、正则性和自由边界的性质及其极限形态等问题。本文的研究分为两个方面：整体实施永久ESOs和非限制实施永久ESOs。整体实施是指,经理人要么不实施其持有的ESOs,要么一次性实施其持有的全部ESOs。而在非限制实施情况下,经理人在任意可实施时刻可以实施其持有的任意份ESOs。首先,我们采用经理人的财富效用最大化方法来研究整体实施情况下的一个永久ESOs定价模型,这是一个带效用函数的永久美式看涨期权的自由边界问题,其值函数和最优实施策略不仅与股价有关,而且还与ESOs的数量有关。其值函数是一个退化的抛物型变分不等式的定解问题的解。对于整体实施情况下的ESOs问题,目前已有许多学者进行了研究,但大多数研究均是基于定性分析或数值计算,没有严格的理论结果。Kadam等(2005)[14]虽然在基于效用的模型中给出了永久ESOs价值的解析解,但他们只考虑一份ESOs,相应的值函数只与股价有关。因为效用函数是非线性函数,经理人所持有的ESOs的总价值不是ESOs数目的线性函数。因此,假设经理人只持有一份ESOs是不合理的。我们用财富效用最大化方法对整体实施情况下的永久ESOs问题建立了一个最优停时模型,其值函数是ESOs数目和股价的函数。利用最优停时理论,我们导出值函数满足一个退化的抛物型变分不等式的定解问题。然后通过切片法,即对变量τ(ESOs数目与风险厌恶系数的乘积)离散化的方法来研究该抛物型变分不等式的定解问题。我们得出了解的存在性、唯一性和正则性,证明了自由边界(最佳实施边界)的连续性、单调性和有关极限形态。其次,我们研究非限制实施情况下的永久ESOs模型。Rogers和Scheinkman(2007)[49]通过经理人的财富效用最大化方法,对非限制实施情况下的具有有限到期日的ESOs问题,建立了一个随机最优控制模型,并获得了相应的抛物型变分不等式的定解问题。但他们对该定解问题没有给出严格的理论研究,只是通过数值分析给出经理人的最优实施策略及相应的一些性质。我们在Rogers和Scheinkman(2007)的模型的基础上,研究相应的永久ESOs模型。通过随机最优控制理论,我们得到其值函数满足一个退化抛物型变分不等式的定解问题。由于该变分不等式的障碍条件里含有值函数关于变量τ(ESOs数目与风险厌恶系数的乘积)的偏导数,这使得对该变分不等式定解问题的理论研究有很大难度。我们仍通过切片法来研究该问题,证明了解的存在性、正则性及解的其他一些性质。最后,我们还对两种实施情况进行数值分析。通过偏微分方程数值解法对经理人的最佳实施边界进行分析和比较。
[Abstract]:The executive option, called ESOs, is a kind of American call option that is paid to managers or employees by the company. Since the mid 1980s, ESOs has become an important part of the compensation of executives in the United States and other countries,.ESOs can be seen as the cost of payment by the company from the manager or employee. Due to the number of ESOs distribution In order to give the reasonable value of ESOs, it is necessary to rationally predict the future implementation strategy of the manager. Because the company executives are unable to sell short company shares (illegal), managers can not construct a combination of company stock, ESOs and riskless bonds to hedge the risk of ESOs. In fact, this is an incomplete market, which makes the no arbitrage pricing method can not be used to price ESOs.
In this paper, we mainly study the solution of a parabolic variational inequality related to the optimal implementation strategy of permanent ESOs in financial markets. Through strict mathematical analysis, we study the existence, uniqueness, regularity and the nature of the free boundary and the limit state of the corresponding solutions. This paper is divided into two aspects: The overall implementation of permanent ESOs and non restrictive implementation of permanent ESOs. means that the manager either does not carry out the ESOs it owns, or implements all the ESOs. it holds in one time. In the unrestricted implementation, the manager can implement any ESOs. that it holds at any time of implementation.
First, we use the manager's wealth utility maximization method to study a permanent ESOs pricing model under the overall implementation. This is the free boundary problem of a permanent American call option with utility function. The value function and the optimal implementation strategy are not only related to the stock price, but also related to the number of ESOs. The solution to the solution of a degenerate parabolic variational inequality has been studied by many scholars at present, but most of the studies are based on qualitative analysis or numerical calculation, no strict theoretical results, such as.Kadam (2005) [14], although the permanent ESOs is given in the utility based model. The analytic solution of the value, but they only consider a ESOs, the corresponding value function is only related to the stock price. Because the utility function is a nonlinear function, the total value of the manager's ESOs is not the linear function of the number of ESOs. Therefore, it is unreasonable to assume that the manager only holds a share of ESOs. We use the method of wealth utility maximization to implement the whole In the case of the perpetual ESOs problem, an optimal stopping time model is established, whose value function is the number of ESOs and the function of the stock price. By using the optimal stopping time theory, we derive the value function to satisfy a degenerate parabolic variational inequality, and then through the slicing method, that is, the variable tau (the product of the number of ESOs and the risk aversion coefficient) is discrete. We study the solution of the parabolic variational inequalities. We obtain the existence, uniqueness and regularity of the understanding, and prove the continuity, monotonicity and the related limit form of the free boundary (the best implementation boundary).
Secondly, we study the permanent ESOs model.Rogers and Scheinkman (2007) [49] under the unrestricted implementation. By the manager's wealth utility maximization method, we establish a stochastic optimal control model for the ESOs problem with limited maturity, and obtain the corresponding solution of the corresponding parabolic variational inequalities. But they do not give strict theoretical research to the problem of the solution, but give the manager's optimal implementation strategy and some corresponding properties by numerical analysis. On the basis of Rogers and Scheinkman (2007) model, we study the corresponding permanent ESOs model. By the stochastic optimal control theory, we get its value function full. Due to the partial derivative of the value function of the variable tau (the product of ESOs number and the risk aversion coefficient) in the barrier condition of the variational inequality, it makes it difficult for the theoretical study of the solution of the variational inequality. We still study the problem by the slicing method. Prove the existence, regularity and some other properties of the solution.
Finally, we carry out numerical analysis of the two implementation cases, and analyze and compare the best implementation boundaries of managers by partial differential equation numerical method.
【学位授予单位】：苏州大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F830.9;F224

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