Optimal Stopping at Random Intervention Times
语 言 英文
We propose a Markovian model to value American-style complete contracts of agents who are temporarily inattentive. Exercise decisions maximizing the contract’s payoff are not admissible continuously but at random intervention times. Further, premature forced exercises events can occur randomly accounting for e.g. liquidity needs or mortality. Exercise events are modeled with possibly market and time dependent arrival intensities. We state the fair contract value in terms of an optimal stopping problem. It is converted to optimal control which, further, provides a characterization in terms of a partial integro differential equation. We suggest the three numerical approaches, forward improvement iteration, least squares Monte-Carlo and finite differences, each corresponding one particular characterization of the value. Our adapted least squares Monte-Carlo method can treat complex and possibly multi-dimensional settings.