Strategies for Milestone-driven Start-ups

New venture start-ups need to “survive” through multiple stages of reaching milestone targets. This work investigates the strategies for start-ups in a milestone-oriented setting by examining a model of a new venture, 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 an upper boundary or a lower one, the start-up firm succeeds or fails. This work solves for the optimal policy and provides an explicit characterization of its structure. In particular, the optimal policy only uses activities from a set characterized by a so-called efficient frontier curve that orders the activities by intuitive metrics. A unique feature of the 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.