Based on the assumption that the long-term value of a venture capital satisfies the algebraic Brownian motion, we develop a continuous-time exit model of venture capital under different exit modes, namely, initial public offering (IPO) and mergers and acquisitions (M&A). The employee incentive problem is analyzed jointly with the exit decision of the firm in terms of the exit timing and the exit mode. Further, the problem of capital exit is considered from two perspectives, namely, optimal venture capital and social welfare maximization, and the differences between these exit decisions are compared. Our model predicts that the timing of an IPO, the purpose of which is to maximize the utility of the capitalists, lags behind the exit timing, whose purpose is to maximize social welfare. Using a numerical analysis, this paper also proves that increasing the production efficiency, lowering the interest rates, and improving risk management can make the exit decision of venture capitalists converge with that of maximizing social welfare.

中文翻译：

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连续时间基于线性合同的风险投资退出决策：IPO或并购

基于风险资本的长期价值满足代数布朗运动的假设，我们建立了不同退出模式下的风险资本的连续时间退出模型，即首次公开募股（IPO）和并购（M＆A） ）。从退出时机和退出方式两方面，结合公司的退出决策对员工激励问题进行了分析。此外，从最优风险投资和社会福利最大化两个角度考虑了资本退出问题，并比较了这些退出决策之间的差异。我们的模型预测，首次公开募股的时机（其目的是使资本家的效用最大化）落后于退出时机（其目的是使社会福利最大化）。通过数值分析