Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect

Jiajia Chang, Zhijun Hu and Hui Yang
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Jiajia Chang: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Zhijun Hu: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
Hui Yang: School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China

Mathematics, 2020, vol. 8, issue 1, 1-16

Abstract: 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.

Keywords: venture capitalist; ambiguity sharing; effort complementarity; pay-performance sensitivity; relative performance evaluation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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