等级制度中的连续时间激励
Continuous-time incentives in hierarchies
摘要：
本文研究了一个层次问题中的连续时间最优契约，该层次问题推广了Sung（2015）的模型。该层次模型由一系列相互关联的委托代理问题，导致一系列的斯塔克伯格均衡。更准确地说，委托人可以与经理人签订合同，激励他们按照自己的最大利益行事，尽管只观察整个层级的净收益。经理们反过来又与他们下面的代理人打交道。代理人和管理者在连续时间内独立控制代表其结果的随机过程。首先，我们通过一个连续的时间适应宋的模型，即使代理人只控制他们的结果的漂移，他们的经理控制他们的持续效用的波动性。这第一个简单的例子证明了最近的结果使用最佳合同的漂移和波动控制，因此，二阶向后随机微分方程的理论，本文的理论部分，致力于一个更一般的模型。我们概述的综合方法突出了考虑连续时间模型的好处，并开辟了获得比较静态的途径。我们还解释了如何将该模型扩展到一个大规模的委托代理层次结构。由于当事人的问题可以简化为只有一个$m$维的状态空间和一个$2m$维的控制集，其中$m$是直接在她之下的经理的数量，因此与这些经理之下的层次结构的大小无关，问题的维度不会爆炸。
英文摘要：
This paper studies continuous-time optimal contracting in a hierarchy problem which generalises the model of Sung (2015). The hierarchy is modeled by a series of interlinked principal-agent problems, leading to a sequence of Stackelberg equilibria. More precisely, the principal can contract with the managers to incentivise them to act in her best interest, despite only observing the net benefits of the total hierarchy. Managers in turn subcontract with the agents below them. Both agents and managers independently control in continuous time a stochastic process representing their outcome. First, we show through a continuous-time adaptation of Sung's model that, even if the agents only control the drift of their outcome, their manager controls the volatility of their continuation utility. This first simple example justifies the use of recent results on optimal contracting for drift and volatility control, and therefore the theory of second-order backward stochastic differential equations, developed in the theoretical part of this paper, dedicated to a more general model. The comprehensive approach we outline highlights the benefits of considering a continuous-time model and opens the way to obtain comparative statics. We also explain how the model can be extended to a large-scale principal-agent hierarchy. Since the principal's problem can be reduced to only an $m$-dimensional state space and a $2m$-dimensional control set, where $m$ is the number of managers immediately below her, and is therefore independent of the size of the hierarchy below these managers, the dimension of the problem does not explode.
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