Venture Capital Problem In Continuous Time—Optimal Investment And Optimal Effort

This paper studies the optimal investment and optimal effort in venture capital,constructs a continuous-time venture investment model,and uses the Hamilton-Jacobi-Bellman equation to obtain the continuous time without considering effort and continuous consideration.While making efforts and considering bilateral efforts,under three different situations,risk investors and venture entrepreneurs have their own optimal decisions and expected returns on risk projects.The results of the model solution are compared,analyzed and numerically simulated.The research shows that: 1.The optimal investment cash flow,optimal effort,and venture entrepreneur 's optimal effort of the venture investor decrease with the potential risk of the risk project and the expected return of the venture investor;with the investment(effort)on the state of the enterprise And the profit rate of risky projects is increasing.2.Collaborative cooperation makes the investment level of investment(effort)of venture investors and venture entrepreneurs and the expected return from risk projects at the same time.Third,only when the proportion of equity is greater than that of the risk investor,will the willingness to incentivize the venture entrepreneur,and the incentive can effectively improve the effort level of the venture entrepreneur and increase the expected return of the entire risk project and both parties involved.4.The efforts of venture investors do not affect the optimal strategy of other factors,but can increase the expected returns of venture investors and venture entrepreneurs.The innovation of this paper: 1.Establish a continuous-time model to study the optimal investment and optimal effort of venture capital.Second,unlike the principal-agent perspective on which general venture capital research is based,this paper studies a variety of different game situations for venture investors and venture entrepreneurs throughout the venture capital process.3.Introduce the efforts of venture investors,study the issue of venture capital considering bilateral efforts,and clarify the importance of venture investors' active management for venture investment.