Investment Under a Disruptive Risk with Costly Bayesian Learning

We study a sequential decision problem in which a firm has the option to invest in a project and can learn about the future profitability of this project prior to investment. The decision process is split into two stages. In the first stage the firm decides whether and how much to invest in learning about the likelihood of a potential disruptive event. The firm pays a learning cost, which depends on the intensity of learning, if the firm decides to invest in learning. Thereafter, it decides when and whether to stop learning and initiate the project by paying a sunk cost. We find that the option to learn is most valuable when it is unclear at the start whether the firm should invest or abandon, i.e. when the revenue flow is average. Then, it is crucial to know whether the disruptive event is likely to arrive soon or not in order to make the optimal decision, hence the firm invests most in learning. The decision to invest in learning is also strongly driven by the range of possible values for the arrival rate of the disruptive event, with investment in learning higher if the range of rates is larger. Furthermore, whether a learning investment is attractive to the firm depends strongly on the prior belief about the arrival rate of the disruptive event. A firm's optimal learning rate is non-monotonic in the firm's learning efficiency. The firm increases its learning rate to decrease its likelihood of making Type I or Type II errors. However, at a certain point, a firm with a higher learning efficiency invests less in learning to save on learning costs. Despite the optimal learning rate being non-monotonic in the learning efficiency, both the probability of making a Type I or II error and the time the firm needs to take a decision decrease monotonically with the learning efficiency.