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摘要翻译：
我们考虑了具有连续支付和终止时一次付清的随机期限委托代理问题的一般形式。在这个问题的欧洲版本中，随机水平完全由委托人选择，除了对输出过程的动力学施加努力之外，代理人没有其他可能的行动。我们还考虑了美国版本的合同，它涵盖了开创性的Sannikov模型，其中代理人也可以通过最优选择合同终止时间来退出。我们的主要结果将这类非零和随机微分对策归结为适当的随机控制问题，可以用随机控制理论的标准方法来解决。这种减少是通过遵循Sannikov的方法得到的，Cvitanic，Possamai和Touzi进一步发展的方法。我们首先引入了一类适当的契约，在这类契约中，代理人的最优努力立即被随机控制理论中的标准验证论证所表征。然后，我们证明了这类契约在适当的意义上是稠密的，因此对这类约束契约族的最优化不会失去一般性。该结果是利用随机时域二阶倒向SDE最近的适定性结果得到的。
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英文标题：
《Random horizon principal-agent problem》
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作者：
Yiqing Lin, Zhenjie Ren, Nizar Touzi, Junjian Yang
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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：General Economics 一般经济学
分类描述：General methodological, applied, and empirical contributions to economics.
对经济学的一般方法、应用和经验贡献。
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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英文摘要：
We consider a general formulation of the random horizon Principal-Agent problem with a continuous payment and a lump-sum payment at termination. In the European version of the problem, the random horizon is chosen solely by the principal with no other possible action from the agent than exerting effort on the dynamics of the output process. We also consider the American version of the contract, which covers the seminal Sannikov's model, where the agent can also quit by optimally choosing the termination time of the contract. Our main result reduces such non-zero-sum stochastic differential games to appropriate stochastic control problems which may be solved by standard methods of stochastic control theory. This reduction is obtained by following Sannikov's approach, further developed by Cvitanic, Possamai, and Touzi. We first introduce an appropriate class of contracts for which the agent's optimal effort is immediately characterized by the standard verification argument in stochastic control theory. We then show that this class of contracts is dense in an appropriate sense so that the optimization over this restricted family of contracts represents no loss of generality. The result is obtained by using the recent well-posedness result of random horizon second-order backward SDE.
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PDF链接：
https://arxiv.org/pdf/2002.10982
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