An integral equation for American put options on assets with general dividend processes

The difference between an American put option and its European counterpart has been characterized in terms of a simple integral expression which can be used to calculate the optimal exercise boundary in a recursive manner, if Black-Scholes dynamics are assumed for the underlying asset. In this paper, we extend this formula to the case where a more general stock and cumulative dividend process are included, and show how this changes the properties of the optimal exercise boundary