Using an option pricing approach, this paper develops a model of a firm’s optimal investment strategy when confronted with a sequence of technological innovations. There are several key features of the model. First, successive innovations of technology are stochastic in both their arrival times, as well as in their profitability. Second, we incorporate the feature of “learning by doing” in that firms choosing to adopt a current innovation become better able to reap the benefits of future innovations. Third, rather than assuming that current innovations disappear when newer innovations arrive, our model more realistically assumes that the previous generation of technology remains a viable market alternative, perhaps at a discounted cost. These features of the model induce a “path dependency” into the firm’s operating options; two firms facing the same choice will choose differently because of past adoption decisions. The model yields four potential migration strategies: the Compulsive strategy where firms adopt every innovation; the Leapfrog strategy where firms bypass the current innovation, but adopt the future innovation; the Buy-and-Hold strategy where firms adopt the current innovation, but fail to cash in on their learning by doing; and the Laggard strategy where firms bypass the current innovation, but adopt it later when the future innovation emerges. The model provides closed-form solutions for the probability that each strategy will be adopted. We then analyze the impact of key underlying variables and distinguish the factors which drive one strategy to dominate another. These implications are discussed and compared with observed firm behavior.