为多阶段里程碑创业公司提供最优策略框架,用风险与成本效益筛选活动。
Strategies for Milestone-driven Start-ups in Multi-activity Settings

- 基于扩散过程建模,通过风险-收益和成本-收益比筛选最优活动组合。
- 首次揭示不同类型的高效前沿曲线,导致策略结构发生质变。
- 适合研究创业决策、动态资源配置的学者与创业者参考。
初创企业需在多个里程碑阶段中存活下来。本文研究了以里程碑为导向的创业企业策略。构建了一个企业家企业状态由扩散过程刻画的模型,企业家可在多种活动中选择(即控制),不同活动带来不同的成本,并决定过程的漂移和方差。当过程达到固定上界则成功,达到下界则失败。具有三个或更多控制的连续时间随机模型通常极难处理。本文完全求解了最优策略,并明确给出了其结构特征:最优策略仅使用由所谓高效前沿曲线定义的一组控制,该曲线按两个直观指标对控制进行排序:风险性(漂移-波动率比)和成本效益(漂移-成本比)。模型的一个独特之处在于,根据参数不同,高效前沿曲线可呈现不同类型,从而导致最优策略结构出现定性差异。据我们所知,这是首个分析可呈现不同类型高效前沿曲线的随机控制模型的研究。本工作为创业企业提供了直观的活动评估标准,并揭示了在里程碑导向情境下,最优策略如何随具体情景发生质变,为创业决策研究奠定了基础。
原文摘要 · Abstract (English)
New venture start-ups need to ``survive'' through multiple stages of reaching milestone targets. We investigate the strategies for start-ups in a milestone-oriented setting. We examine a model of an entrepreneurial start-up firm, where its state is captured by a diffusion process. The entrepreneur can choose between multiple activities (or controls), which incur different cost and determine the drift and the variance of the process. Depending on whether the process reaches a fixed upper boundary or a lower one, the start-up firm succeeds or fails. Continuous-time stochastic models with multiple ($\ge 3$) controls are typically very challenging to deal with. In this work, we are able to completely solve for the optimal policy and provide an explicit characterization of its structure. In particular, the optimal policy only uses controls from a set characterized by a so-called efficient frontier curve that orders the controls by two intuitive measures: riskiness (drift-to-volatility ratio) and cost-effectiveness (drift-to-cost ratio). A unique feature of our model is that depending on the model parameters, the efficient frontier curves can be of different types, resulting in qualitatively different structures of the optimal policy. As far as we know, this is the first study that analyzes a stochastic control model which admits efficient frontier curves of different types. Our work provides start-up firms with intuitive measures to evaluate their activities and offers valuable insights on how the optimal strategies in a milestone-oriented setting change qualitatively contingent upon the specific scenario. We believe the results provide a foundational block in the study of entrepreneurial decision-making.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。