On the American Put Option with Ambiguity

Owing to ambiguity in markets, this article introduces a generalized model to price the American put option with multiple priors in continuous time. Under some feasible conditions, the problem of American put option under ambiguity can be reduced to a pertinent free boundary problem in a Markovian setting. We can give a conservative evaluation for the American option under ambiguity, since the size of k-ignorance can be estimated by the historical data. Our methods show an effective optimal timing strategy against the stock price behavior and ambiguity aversion.