$C^{1,1}$ regularity for principal-agent problems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913222585483264 |
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| author | McCann, Robert J. Rankin, Cale Zhang, Kelvin Shuangjian |
| author_facet | McCann, Robert J. Rankin, Cale Zhang, Kelvin Shuangjian |
| contents | 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 The original ideas for this proof arise from an earlier, unpublished, result of Caffarelli and Lions for bilinear preferences which we extend here to general quasilinear benefit functions.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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04937 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $C^{1,1}$ regularity for principal-agent problems McCann, Robert J. Rankin, Cale Zhang, Kelvin Shuangjian Analysis of PDEs Optimization and Control 49N60, 91B43 (Primary) 35R35, 52A41, 58E50, 90B5 (Secondary) 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 The original ideas for this proof arise from an earlier, unpublished, result of Caffarelli and Lions for bilinear preferences which we extend here to general quasilinear benefit functions.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. |
| title | $C^{1,1}$ regularity for principal-agent problems |
| topic | Analysis of PDEs Optimization and Control 49N60, 91B43 (Primary) 35R35, 52A41, 58E50, 90B5 (Secondary) |
| url | https://arxiv.org/abs/2303.04937 |