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Abstract
The last couple of years has seen a remarkable number of new, explicit examples of the Wiener.Hopf factorization for Levy processes where previously there had been very few. We mention, in particular, the many cases of spectrally negative Levy processes in [Sixth Seminar on Stochastic Analysis, Random Fields and Applications (2011) 119.146, Electron. J. Probab. 13 (2008) 1672.1701], hyperexponential and generalized hyperexponential Levy processes [Quant. Finance 10 (2010) 629.644], Lampertistable processes in [J. Appl. Probab. 43 (2006) 967.983, Probab. Math. Statist. 30 (2010) 1.28, Stochastic Process. Appl. 119 (2009) 980.1000, Bull. Sci. Math. 133 (2009) 355.382], Hypergeometric processes in [Ann. Appl. Probab. 20 (2010) 522.564, Ann. Appl. Probab. 21 (2011) 2171.2190, Bernoulli 17 (2011) 34.59], βprocesses in [Ann. Appl. Probab. 20 (2010) 1801.1830] and θprocesses in [J. Appl. Probab. 47 (2010) 1023.1033]. In this paper we introduce a new family of Levy processes, which we call Meromorphic Levy processes, or just Mprocesses for short, which overlaps with many of the aforementioned classes. A key feature of the Mclass is the identification of theirWiener.Hopf factors as rational functions of infinite degree written in terms of poles and roots of the Laplace exponent, all of which are real numbers. The specific structure of the Mclass Wiener.Hopf factorization enables us to explicitly handle a comprehensive suite of fluctuation identities that concern first passage problems for finite and infinite intervals for both the process itself as well as the resulting process when it is reflected in its infimum. Such identities are of fundamental interest given their repeated occurrence in various fields of applied probability such as mathematical finance, insurance risk theory and queuing theory.
Original language  English 

Pages (fromto)  11011135 
Number of pages  35 
Journal  Annals of Applied Probability 
Volume  22 
Issue number  3 
DOIs  
Publication status  Published  Jun 2012 
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 1 Finished

LEVY PROCESSES OPTIMAL STOPPING PROBLEMS AND STOCHASTIC GAME S
Kyprianou, A.
Engineering and Physical Sciences Research Council
1/01/07 → 31/12/09
Project: Research council