We model the creation of a new venture with a drift-variance stochastic control framework in which the state of the venture is captured by a diffusion process. The entrepreneur creating the venture chooses costly controls, which determine both the drift and the variance of the process. When the process reaches an upper boundary, the venture succeeds and the entrepreneur receives a reward. When the process reaches a lower boundary, the venture fails. The entrepreneur can choose between different controls and wishes to maximize the expected total reward minus total cost. We derive closed-form expressions under which the optimal policy will be dynamic versus static and we prove that when the policy is dynamic it switches between the two controls at most once. The results reveal a subtle trade-off between the cost of the two controls, their drift and their variances, in which controls that are more expensive may be utilized more than controls that are less expensive.
