论文标题
高斯代理机构的记忆和线性合同问题
Gaussian Agency problems with memory and Linear Contracts
论文作者
论文摘要
当代理控制表现出记忆的过程时，委托人仍然可以提供最佳的动态合同吗？我们通过考虑一般的高斯环境，即输出动力学不一定是半木星或马尔可夫过程，我们提供了一个积极的答案。我们介绍了一类丰富的主体代理模型，这些模型包括带有内存的动态代理模型。从数学的角度来看，我们开发了一种方法来处理控制问题的可能的非马克维亚性和非偏移性，这不能再通过通常的汉密尔顿 - 雅各布利 - 贝尔曼方程来直接解决。我们的主要贡献是表明，对于一维模型，此设置始终允许在可观察到的最佳结局中以确定性的最佳努力级别获得最佳的线性合同。在较高的维度中，我们表明，当工作成本功能是径向的时，线性合同仍然是最佳的，并且我们量化了线性合同和最佳合同之间的差距，以实现更一般的二次努力成本。
Can a principal still offer optimal dynamic contracts that are linear in end-of-period outcomes when the agent controls a process that exhibits memory? We provide a positive answer by considering a general Gaussian setting where the output dynamics are not necessarily semi-martingales or Markov processes. We introduce a rich class of principal-agent models that encompasses dynamic agency models with memory. From the mathematical point of view, we develop a methodology to deal with the possible non-Markovianity and non-semimartingality of the control problem, which can no longer be directly solved by means of the usual Hamilton-Jacobi-Bellman equation. Our main contribution is to show that, for one-dimensional models, this setting always allows for optimal linear contracts in end-of-period observable outcomes with a deterministic optimal level of effort. In higher dimension, we show that linear contracts are still optimal when the effort cost function is radial and we quantify the gap between linear contracts and optimal contracts for more general quadratic costs of efforts.
