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We consider the impact of ambiguity on the optimal timing of a class oftwo-dimensional integral option contracts when the exercise payoff is apositively homogeneous measurable function. Hence, the considered class ofexercise payoffs includes discontinuous functions as well. We identify aparameterized family of excessive functions generating an appropriate class ofsupermartingales for the considered problems and then express the value of theoptimal policy as well as the worst case measure in terms of these processes.The advantage of our approach is that it reduces the analysis of themultidimensional problem to the analysis of an ordinary one-dimensional staticoptimization problem. In that way it simplifies earlier treatments of theproblem without ambiguity considerably. We also illustrate our findings inexplicitly parameterized examples.

The Impact of Ambiguity on the Optimal Exercise Timing of Integral Option Contracts