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

## TL;DR

This paper investigates how ambiguity influences the optimal exercise timing of two-dimensional integral option contracts with various payoff functions, simplifying complex multidimensional problems to one-dimensional static optimization.

## Contribution

It introduces a parameterized family of supermartingales to analyze the problem, reducing multidimensional ambiguity issues to a simpler one-dimensional framework.

## Key findings

- Explicit characterization of the value and worst-case measure.
- Simplification of multidimensional problems to one-dimensional optimization.
- Application to parameterized examples demonstrating the approach.

## Abstract

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.