  We consider the impact of ambiguity on the optimal timing of a class of
two-dimensional integral option contracts when the exercise payoff is a
positively homogeneous measurable function. Hence, the considered class of
exercise payoffs includes discontinuous functions as well. We identify a
parameterized family of excessive functions generating an appropriate class of
supermartingales for the considered problems and then express the value of the
optimal 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 the
multidimensional problem to the analysis of an ordinary one-dimensional static
optimization problem. In that way it simplifies earlier treatments of the
problem without ambiguity considerably. We also illustrate our findings in
explicitly parameterized examples.
