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Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect

Author

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  • Jiajia Chang

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
    School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China)

  • Zhijun Hu

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
    School of Management, Guizhou University, Guiyang 550025, China)

  • Hui Yang

    (School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China)

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.

Suggested Citation

  • Jiajia Chang & Zhijun Hu & Hui Yang, 2020. "Venture Capital Contracting with Ambiguity Sharing and Effort Complementarity Effect," Mathematics, MDPI, vol. 8(1), pages 1-16, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:140-:d:310763
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    References listed on IDEAS

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