Contraction options and optimal multiple-stopping in spectrally negative Levy models

TL;DR

This paper addresses the optimal multiple-stopping problem for projects modeled by spectrally negative Levy processes, providing solutions for threshold-type stopping times and demonstrating the approach's effectiveness through numerical experiments.

Contribution

It extends the classical model to spectrally negative Levy processes and derives explicit solutions for multi-stage stopping problems using scale functions.

Findings

Optimal stopping times are of threshold-type.

The value function can be expressed via scale functions.

Numerical experiments confirm the method's efficiency.

Abstract

This paper studies the optimal multiple-stopping problem arising in the context of the timing option to withdraw from a project in stages. The profits are driven by a general spectrally negative Levy process. This allows the model to incorporate sudden declines of the project values, generalizing greatly the classical geometric Brownian motion model. We solve the one-stage case as well as the extension to the multiple-stage case. The optimal stopping times are of threshold-type and the value function admits an expression in terms of the scale function. A series of numerical experiments are conducted to verify the optimality and to evaluate the efficiency of the algorithm.