Work

Beating the omega clock: An optimal stopping problem with random time-horizon under spectrally negative Lévy models

Year: 2018

Type: article

Abstract: We study the optimal stopping of an American call option in a random time-horizon under exponential spectrally negative Lévy 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 Lévy process below a level $y$, exceeds an independent exponential random variable with mean $1/q>0$. 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.

Source: The Annals of Applied Probability

DOI: 10.1214/17-aap1322

Authors: Neofytos Rodosthenous, Hongzhong Zhang

Institutions: University of London, Columbia University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: Engineering and Physical Sciences Research Council

Awards: G2201079836, Optimal timing for financial and economic decisions under adverse and stressful conditions