# A Solvable Two-dimensional Optimal Stopping Problem in the Presence of Ambiguity

## TL;DR

This paper explores how ambiguity influences optimal stopping times in a multidimensional setting, revealing that ambiguity affects both growth and discount rates, which is a novel insight not present in one-dimensional models.

## Contribution

It introduces a multidimensional model showing that ambiguity impacts both growth and discount rates, providing a new perspective on optimal timing under uncertainty.

## Key findings

- Ambiguity affects the rate of growth of underlying processes.
- Ambiguity influences the discount rate in the model.
- Multidimensional setting reveals effects not seen in one-dimensional models.

## Abstract

According to conventional wisdom, ambiguity accelerates optimal timing by decreasing the value of waiting in comparison with the unambiguous benchmark case. We study this mechanism in a multidimensional setting and show that in a multifactor model ambiguity does not only influence the rate at which the underlying processes are expected to grow, it also affects the rate at which the problem is discounted. This mechanism where nature also selects the rate at which the problem is discounted cannot appear in a one-dimensional setting and as such we identify an indirect way of how ambiguity affects optimal timing.