Optimal Exercise Decisions under Inattention

Abstract

In decision problems, frictions as well as constraints play an increasingly important role. Especially, optimal timing problems can be affected by potentially “non-rational” behavior of the decision maker which is not incorporated in the standard theory. A relevant problem of this kind is the real option to abandon a project. Limited cognitive resources and external restrictions to option exercise may result in a suboptimal outcome. The term inattention can summarize such frictions and constraints. In this paper, we address this issue by proposing a Markovian model to value American-style contracts of agents who are temporarily inattentive. Exercise decisions maximizing the contract’s payoff are not admissible continuously but at random intervention times arriving with possibly state and time dependent intensities. An optimal stopping problem provides the contract value. It is converted to optimal control which, given sufficient regularity, induces a characterisation in terms of a partial integro differential equation. We consider three numerical approaches, forward improvement iteration, least squares Monte-Carlo and finite differences, each corresponding to one particular characterization of the contract value. Our adapted least squares Monte-Carlo method can treat complex and possibly multi-dimensional settings.

Keywords: Markov processes, optimal stopping, optimal control, random intervention times, inattention, least squares Monte-Carlo, forward improvement iteration