摘要翻译：
本文研究了一个层次问题中的连续时间最优合同问题，推广了Sung(2015)的模型。该层次结构是由一系列相互联系的委托-代理问题构成的，导致了一系列Stackelberg均衡。更准确地说，校长可以与经理签订合同，激励他们为她的最佳利益行事，尽管只观察总层级的净效益。经理们反过来又与他们下面的代理人分包。代理人和管理者都独立地在连续时间内控制一个代表他们结果的随机过程。首先，我们通过对Sung模型的连续时间适应性证明，即使代理人只控制其结果的漂移，其管理者也控制其持续效用的波动性。第一个简单的例子证明了对漂移和波动控制的最优契约的最新结果的使用，因此，在本文理论部分发展的二阶倒向随机微分方程理论致力于一个更一般的模型。我们概述的综合方法强调了考虑连续时间模型的好处，并为获得比较静力学开辟了道路。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。由于主体的问题可以被简化为一个$m$维的状态空间和一个$2m$维的控制集，其中$m$是紧接她下面的管理器的数量，因此与这些管理器下面的层次结构的大小无关，所以问题的维度不会爆炸。
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英文标题：
《Continuous-time incentives in hierarchies》
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作者：
Emma Hubert
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最新提交年份：
2020
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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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PDF链接：
https://arxiv.org/pdf/2007.10758