Contraction Options and Optimal Multiple-Stopping in Spectrally Negative Lévy Models

Journal Article · Sat Aug 15 00:00:00 EDT 2015 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-014-9274-0· OSTI ID:22469889

Yamazaki, Kazutoshi ^[1]

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1. Kansai University, Department of Mathematics, Faculty of Engineering Science (Japan)

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 Lévy 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.

• OSTI ID: 22469889
• Journal Information: Applied Mathematics and Optimization, Vol. 72, Issue 1; Other Information: Copyright (c) 2015 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
BROWNIAN MOVEMENT
CONTRACTION
EFFICIENCY
FUNCTIONS
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS