The Perpetual American Put Option for Jump-Diffusions

Abstract

We solve a specific optimal stopping problem with an infinite time horizon, when the state variable follows a jump-diffusion. The novelty of the paper is related to the inclusion of a jump component in this stochastic process. Under certain conditions, our solution can be interpreted as the price of an American perpetual put option. We characterize the continuation region when the underlying asset follows this type of stochastic process. Our basic solution is exact only when jump sizes cannot be negative. A methodology to deal with negative jump sizes is also demonstrated. Energy, Natural Resources and Environmental Economics Energy, Natural Resources and Environmental Economics Look