一个退出合约优化问题
An exit contract optimization problem
AI总结：
本文研究面向多个异质代理人的通用退出合约设计问题，利用Bank-El Karoui表示将其转化为最优控制与多重停时问题，证明最优合约存在，并给出离散时间逼近及马尔可夫/连续合约类上的讨论。
摘要：
我们研究一个退出合约设计问题，其中一方为多个异质代理人提供一份通用退出合约，每个代理人根据该合约选择一个最优（退出）停时。问题在于针对某个依赖于合约以及代理人退出时间的准则来优化该通用退出合约。在一个技术性单调性条件下，并利用Bank-El Karoui对随机过程的表示，我们能够将最初的合约优化问题转化为一个最优控制问题。后者还等价于一个最优多重停时问题，并且最优合约的存在性得到了证明。我们接着证明，连续时间情形下的问题可以由一列离散时间问题逼近，这将引出一个自然的数值逼近方法。最后，我们讨论了在所有马尔可夫型和/或连续退出合约类上的优化问题。
英文摘要：
We study an exit contract design problem, where one provides a universal exit contract to multiple heterogeneous agents, with which each agent chooses an optimal (exit) stopping time. The problem consists in optimizing the universal exit contract w.r.t. some criterion depending on the contract as well as the agents' exit times. Under a technical monotonicity condition, and by using Bank-El Karoui's representation of stochastic processes, we are able to transform the initial contract optimization problem into an optimal control problem. The latter is also equivalent to an optimal multiple stopping problem and the existence of the optimal contract is proved. We next show that the problem in the continuous-time setting can be approximated by a sequence of discrete-time ones, which would induce a natural numerical approximation method. We finally discuss the optimaization problem over the class of all Markovian and/or continuous exit contracts.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
