Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect
In this paper, we established a continuous-time agency model in which an ambiguity-averse venture capitalist (VC) employs an ambiguity-neutral entrepreneur (EN) to manage an innovative project. We analyzed the connection between ambiguity sharing and incentives under double moral hazard. Applying a...
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| Format: | Article |
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MDPI AG
2020-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/1/140 |
| _version_ | 1828857743585312768 |
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| author | Jiajia Chang Zhijun Hu Hui Yang |
| author_facet | Jiajia Chang Zhijun Hu Hui Yang |
| author_sort | Jiajia Chang |
| collection | DOAJ |
| description | In this paper, we established a continuous-time agency model in which an ambiguity-averse venture capitalist (VC) employs an ambiguity-neutral entrepreneur (EN) to manage an innovative project. We analyzed the connection between ambiguity sharing and incentives under double moral hazard. Applying a stochastic dynamic programming approach, we solved the VC’s maximization problem and obtained the Hamilton−Jacobi−Bellman (HJB) equation under a special form of the value function. We showed that the optimal pay-performance sensitivity was a fixed point of a nonlinear equation. The model ambiguity on the probability measure induced a tradeoff between ambiguity sharing and the incentive compensation that improved the EN’s pay-performance sensitivity level. Besides, we simulated the model and showed that when two efforts were complementary, the VC’s effort did not monotonically decrease with respect to the pay-performance sensitivity, while the EN’s effort did not monotonically increase in the pay-performance sensitivity level. More importantly, we found that as efforts tended to be more complementary, the optimal pay-performance sensitivity tended to approach those that maximized the efforts exerted by the EN and the VC. |
| first_indexed | 2024-12-13T01:42:57Z |
| format | Article |
| id | doaj.art-6f9f69dfd5c14e86accc7f1db0c98bbd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-13T01:42:57Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6f9f69dfd5c14e86accc7f1db0c98bbd2022-12-22T00:03:42ZengMDPI AGMathematics2227-73902020-01-018114010.3390/math8010140math8010140Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity EffectJiajia Chang0Zhijun Hu1Hui Yang2School of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaSchool of Mathematics and Statistics, Guizhou University, Guiyang 550025, ChinaIn this paper, we established a continuous-time agency model in which an ambiguity-averse venture capitalist (VC) employs an ambiguity-neutral entrepreneur (EN) to manage an innovative project. We analyzed the connection between ambiguity sharing and incentives under double moral hazard. Applying a stochastic dynamic programming approach, we solved the VC’s maximization problem and obtained the Hamilton−Jacobi−Bellman (HJB) equation under a special form of the value function. We showed that the optimal pay-performance sensitivity was a fixed point of a nonlinear equation. The model ambiguity on the probability measure induced a tradeoff between ambiguity sharing and the incentive compensation that improved the EN’s pay-performance sensitivity level. Besides, we simulated the model and showed that when two efforts were complementary, the VC’s effort did not monotonically decrease with respect to the pay-performance sensitivity, while the EN’s effort did not monotonically increase in the pay-performance sensitivity level. More importantly, we found that as efforts tended to be more complementary, the optimal pay-performance sensitivity tended to approach those that maximized the efforts exerted by the EN and the VC.https://www.mdpi.com/2227-7390/8/1/140venture capitalistambiguity sharingeffort complementaritypay-performance sensitivityrelative performance evaluation |
| spellingShingle | Jiajia Chang Zhijun Hu Hui Yang Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect Mathematics venture capitalist ambiguity sharing effort complementarity pay-performance sensitivity relative performance evaluation |
| title | Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect |
| title_full | Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect |
| title_fullStr | Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect |
| title_full_unstemmed | Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect |
| title_short | Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect |
| title_sort | venture capital contracting with ambiguity sharing and effort complementarity effect |
| topic | venture capitalist ambiguity sharing effort complementarity pay-performance sensitivity relative performance evaluation |
| url | https://www.mdpi.com/2227-7390/8/1/140 |
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