Beating the Omega Clock: An Optimal Stopping Problem with Random Time-Horizon Under Spectrally Negative Lévy Models
Annals of Applied Probability
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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 rst 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 > 0. We show that the shape of the value function varies qualitatively with di erent values of q and y. In particular, we show that for certain values of q and y, some quantitatively di erent 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.
AuthorsRODOSTHENOUS, N; Zhang, H
- Applied Mathematics