Optimal Stopping at Random Intervention Times

We propose a Markovian model to value American-style complete contracts of temporarily inattentive agents. Exercise decisions maximizing the contract's payoff are not admissible continuously but at random intervention times.... [ view full abstract ]

We propose a Markovian model to value American-style complete contracts of temporarily inattentive agents. Exercise decisions maximizing the contract's payoff are not admissible continuously but at random intervention times. Premature forced exercise events can occur randomly accounting for e.g. liquidity needs or mortality. We state the contract value in terms of an optimal stopping problem which is converted to optimal control and provides a characterization in terms of a partial integro differential equation. We suggest the three numerical approaches, forward improvement iteration, finite differences and least squares Monte-Carlo, where the latter can treat the most complex and multi-dimensional settings.