Integral Options in Models with Jumps

Abstract

We present an explicit solution to the formulated in [17] optimal stopping problem for a geometric compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problem to an integro-differential free-boundary problem where the smooth fit may break down and then be replaced by the continuous fit. The result can be interpreted as pricing perpetual integral options in a model with jumps.Jump process, stochastic differential equation, optimal stopping problem, integral American option, compound Poisson process, Shiryaev´s process, Girsanov´s theorem, Ito´s formula, integrodifferential free-boundary problem, smooth and continuous fit, hypergeometric functions