Ambiguous Investment under Choquet-Brownian Motion with Neo-Additive Capacities

Abstract

A new branch of the real options literature examines the optimal stopping problem of an investment opportunity embedded in an ambiguous environment as opposed to traditional aleatory risk. Only few articles have been published within this emerging eld. This thesis critically reviews the existing modeling e orts speci ed by MEU, -MEU, and CEU preference relations, and nds that the current speci cations collectively fail to achieve separability of ambiguity and ambiguity preferences in a manner that is coherent with economic intuition. We show that convex combinations in the multiple priors approach aimed at integrating ambiguity attitudes yield peculiar non-monotonic preferences toward ambiguity and cannot be reconciled with dynamic consistency. We propose a speci cation that mends the shortcomings of the current literature by building on the recently developed dynamically consistent Choquet-Brownian motions. We o er an original contribution by introducing neo-additive capacities in order to obtain a proper separation of tastes and beliefs and apply the developed speci cation to the optimal stopping problem of the rm in possession of a real option to invest in order to show that the injection of ambiguity to the economy yields drastically di erent e ects on both project value and option value than under pure risk. Whereas risk increases option value through the continuation region, for an ambiguity averse rm ambiguity lowers option value both in the stopping region and the continuation region, which delays investment as well, but for critically di erent reasons. For an ambiguity loving rm, ambiguity increases option value in both regions, but does so more in the stopping region. In consequence, investment tends to be delayed by pessimistic rms and pulled forward by optimistic rms under ambiguity. Hence, the proposed model resonates in its ndings with the main results of the current literature under -MEU and CEU speci cations, while it by means of the introduction of neo-additive capacities contributes with the possibility of a re ned analysis of the role of ambiguity preferences in guiding the direction of the impact from ambiguity on real option valuation and investment timing. As a result, we provide a well-speci ed explanation of non-identical investment behavior in identical environments due to heterogeneous tastes and beliefs.