Geodesic
The unified form of Pollaczek--Khinchine formula for L\'{e}vy processes with matrix-exponential negative jumps
Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 15-23.

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For Lévy processes with matrix-exponential negative jumps, the unified form of the Pollaczek-Khinchine formula is established.
Keywords: Pollaczek–Khinchine formula; Lévy processes; matrix-exponential negative jumps. 
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D. Gusak; Ie. Karnaukh. The unified form of Pollaczek--Khinchine formula for L\'{e}vy processes with matrix-exponential negative jumps. Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 15-23. http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a2/

[1] S. Asmussen, Applied Probability and Queues, Springer, New York, 2003 | MR | Zbl

[2] S. Asmussen, Ruin Probabilities, World Scientific, Singapore, 2010 | MR | Zbl

[3] A. E. Kyprianou, Introductory Lectures on Fluctuations of Levy Processes with Applications, Springer, New York, 2006 | MR | Zbl

[4] O. Kella, “The class of distributions associated with the generalized Pollaczek–Khinchine formula”, J. of Appl. Prob., 49(3) (2012), 883–887 | DOI | MR | Zbl

[5] M. Huzak et al., “Ruin probabilities and decompositions for general perturbed risk processes”, Annals of Appl Prob., 14:3 (2004), 1378–1397 | DOI | MR | Zbl

[6] D. Gusak, “On some generalization of the Pollaczek–Khinchine formula”, Theory of Stoch. Process., 16(32):1 (2010), 49–56 | MR | Zbl

[7] M. Kwasnicki, J. Malecki, M. Ryznar, “Suprema of Levy processes”, Ann. of Probab., 41:3B (2013), 2047–2065 | DOI | MR | Zbl

[8] L. Chaumont, “On the law of the supremum of Levy processes”, Ann. of Probab., 41:3A (2013), 1191–1217 | DOI | MR | Zbl

[9] A. Kuznetsov, A. E. Kyprianou, J. C. Pardo, “Meromorphic Levy processes and their fluctuation identities”, Ann. of Appl. Prob., 22:3 (2012), 1101–1135 | DOI | MR | Zbl

[10] N. Bratiychuk, D. Husak, Boundary-Values Problems for Processes with Independent Increments, Naukova Dumka, Kyiv, 1990 (in Russian)

[11] A. L. Lewis, E. Mordecki, “Wiener-Hopf factorization for Levy processes having negative jumps with rational transforms”, J. of Appl. Prob., 45:1 (2008), 118–134 | DOI | MR | Zbl

[12] D. Husak, Processes with Independent Increments in Risk Theory, Institute of Mathematics of the NAS of Ukraine, Kyiv, 2011 (in Ukrainian)

[13] J. Bertoin, Levy Processes, Cambridge Univ. Press, Cambridge, 1996 | MR | Zbl

[14] E. Mordecki, “Ruin probabilities for Levy processes with mixed-exponential negative jumps”, Teor. Veroyatn. Primen., 48 (2003), 188–194 | DOI | MR | Zbl

[15] N. Cai, S. G. Kou, “Option pricing under a mixed-exponential jump diffusion model”, Manag. Sci., 57:11 (2011), 2067–2081 | DOI