委托代理问题的正则性

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-06-25 DOI:10.1016/j.aim.2025.110396

Robert J. McCann , Cale Rankin , Kelvin Shuangjian Zhang

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引用次数: 0

摘要

我们证明了解决Figalli， Kim和McCann最初考虑的委托代理问题的一个子类的间接效用的内部C1,1正则性。我们的方法是基于一个合适的比较函数的构造，本质上，它允许人们在抛物线之间捏取解。这一证明的原始思想来自于Caffarelli和Lions关于双线性偏好的早期未发表的结果，我们在这里将其扩展到一般拟线性利益函数。我们给出了一个简单的例子，证明了C1,1正则性是最优的。

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C1,1 regularity for principal-agent problems

We prove the interior

C^{1, 1}

regularity of the indirect utilities which solve a subclass of principal-agent problems originally considered by Figalli, Kim, and McCann. Our approach is based on construction of a suitable comparison function which, essentially, allows one to pinch the solution between parabolas. The original ideas for this proof arise from an earlier, unpublished, result of Caffarelli and Lions for bilinear preferences which we extend here to general quasilinear benefit functions. We give a simple example which shows the

C^{1, 1}

regularity is optimal.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.