Real Options with Uncertain Maturity and Competition

We develop a new approach to dealing with real options problems with uncertain maturity. This type of situation is typical for Ramp;D investments and mine or oil exploration projects. These types of projects are characterized by significant on-going investment costs until completion. Since time to completion is uncertain, the total investment costs will also be uncertain. Despite the fact that these projects include complicated American abandonment/switching options until completion and European options at completion (because of fixed final investment costs) we obtain simple closed form solutions. We apply the framework to situations in which the owner of the project has monopoly rights to the outcome of the project, and to situations in which there are two owners who simultaneously invest, but where only one of them may obtain the rights to the outcome. We expand the real options framework to incorporate game theoretic considerations, including a generalization of mixed strategies to continuous-time models in the form of abandonment intensities