Beating the Omega Clock: An Optimal Stopping Problem with Random Time-Horizon Under Spectrally Negative Lévy Models

The Annals of Applied Probability, Forthcoming

35 Pages Posted: 14 Jun 2017

See all articles by Neofytos Rodosthenous

Neofytos Rodosthenous

Queen Mary, University of London

Hongzhong Zhang

Columbia University

Date Written: June 13, 2017

Abstract

We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative L'evy models. The random time-horizon is modeled as the so-called Omega default clock in insurance, which is the first time when the occupation time of the underlying L'evy process below a level y, exceeds an independent exponential random variable with mean 1/q. We show that the shape of the value function varies qualitatively with different values of q and y. In particular, we show that for certain values of q and y, some quantitatively different but traditional up-crossing strategies are still optimal, while for other values we may have two disconnected continuation regions, resulting in the optimality of two-sided exit strategies. By deriving the joint distribution of the discounting factor and the underlying process under a random discount rate, we give a complete characterization of all optimal exercising thresholds. Finally, we present an example with a compound Poisson process plus a drifted Brownian motion.

Keywords: L'evy process, optimal stopping, Omega clock, occupation times, random discount rate, impatience

JEL Classification: C41, G12

Suggested Citation

Rodosthenous, Neofytos and Zhang, Hongzhong, Beating the Omega Clock: An Optimal Stopping Problem with Random Time-Horizon Under Spectrally Negative Lévy Models (June 13, 2017). The Annals of Applied Probability, Forthcoming , Available at SSRN: https://ssrn.com/abstract=2985493

Neofytos Rodosthenous

Queen Mary, University of London ( email )

School of Mathematical Sciences
Mile End Road
London, E1 4NS
United Kingdom

Hongzhong Zhang (Contact Author)

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
55
Abstract Views
641
Rank
670,186
PlumX Metrics