A0623
Title: Time inconsistent optimal stopping under model ambiguity and financial applications
Authors: Xiang Yu - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Yu-Jui Huang - University of Colorado (United States)
Abstract: An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an alpha-maxmin nonlinear expectation, renders the stopping problem time-inconsistent. We look for subgame perfect equilibrium stopping policies, formulated as fixed points of an operator. We show that any initial stopping policy will converge to equilibrium through a fixed-point iteration for a one-dimensional diffusion with drift and volatility uncertainty. This allows us to capture much more diverse behavior, depending on an agent's ambiguous attitude, beyond the standard worst-case (or best-case) analysis. In a concrete example of real options valuation under model ambiguity, all equilibrium stopping policies and the best one among them are fully characterized under appropriate conditions. It explicitly demonstrates the effect of ambiguity attitude on decision-making: the more ambiguity-averse, the more eager to stop, to withdraw from the uncertain environment. The main result hinges on a delicate analysis of continuous sample paths in the canonical space and the capacity theory. To resolve measurability issues, a generalized measurable projection theorem, new to the literature, is also established.
