References:

[1] J. Bertoin Lévy Processes Cambridge University Press (1996)

[2] J. Bertoin Exponential decay and ergodicity of completely asymmetric Lévy processes in a finite interval Ann. Appl. Probab., 7 (1) (1997), pp. 156–169

[3] R. Biard, S. Loisel, C. Macci, N. Veraverbeke Asymptotic behavior of the finite-time expected time-integrated negative part of some risk processes and optimal reserve allocation J. Math. Anal. Appl., 367 (2) (2010), pp. 535–549


[4] T. Chan, A.E. Kyprianou, M. Savov, Smoothness of scale functions for spectrally negative Lévy processes, Probability Theory and Related Fields (in press).

[5] M. Chesney, M. Jeanblanc-Picqué, M. Yor Brownian Excursions and Parisian barrier options Adv. Appl. Probab., 29 (1) (1997), pp. 165–184

[6] I. Czarna, Z. Palmowski, Ruin probability with Parisian delay for a spectrally negative Lévy risk process, 2010, arXiv:1003.4299v1 [math.PR].

[7] A. Dassios, S. Wu, Parisian ruin with exponential claims, preprint, 2009.

[8] A.E. dos Reis How long is the surplus below zero? Insurance Math. Econom., 12 (1) (1993), pp. 23–38

[9] F. Hubalek, A.E. Kyprianou Old and new examples of scale functions for spectrally negative Lévy processes ,in: R. Dalang, M. Dozzi, F. Russo (Eds.), Sixth Seminar on Stochastic Analysis, Random Fields and Applications, Progress in Probability, Birkhäuser (2010)

[10] K. Itô, H.P. McKean Jr. Diffusion Processes and Their Sample Paths Springer-Verlag, Berlin (1974)

[11] I. Karatzas, S.E. Shreve Brownian Motion and Stochastic Calculus (second edition)Springer-Verlag, New York (1991)

[12] C. Klüppelberg, A.E. Kyprianou On extreme ruinous behaviour of Lévy insurance risk processes J. Appl. Probab., 43 (2006), pp. 594–598

[13] A. Kuznetsov, A.E. Kyprianou, V. Rivero, The theory of scale functions for spectrally negative Lévy processes, 2011, arXiv:1104.1280v1 [math.PR].

[14] A.E. Kyprianou Introductory Lectures on Fluctuations of Lévy Processes with Applications Universitext. Springer-Verlag, Berlin (2006)

[15] A.E. Kyprianou, P. Patie A Ciesielski-Taylor type identity for positive self-similar Markov processes Ann. Inst. H. Poincaré, 47 (3) (2011), pp. 917–928

[16] A.E. Kyprianou, V. Rivero Special, conjugate and complete scale functions for spectrally negative Lévy processes Electron. J. Probab., 13 (2008), pp. 1672–1701

[17] D. Landriault, J.-F. Renaud, X. Zhou, Insurance risk models with Parisian implementation delays, 2010, ssrn.com/abstract=1744193.

[18] R.L. Loeffen, I. Czarna, Z. Palmowski, Parisian ruin probability for spectrally negative Lévy processes, 2011, arXiv:1102.4055v1 [math.PR].

[19] R.L. Loeffen, J.-F. Renaud De Finetti’s optimal dividends problem with an affine penalty function at ruin Insurance Math. Econom., 46 (1) (2010), pp. 98–108

[20] J. Obłój, M. Pistorius On an explicit Skorokhod embedding for spectrally negative Lévy processes J. Theoret. Probab., 22 (2) (2009), pp. 418–440

[21] B.A. Surya Evaluating scale functions of spectrally negative Lévy processes J. Appl. Probab., 45 (1) (2008), pp. 135–149

[22] C. Yin, K. Yuen, Some exact joint laws associated with spectrally negative Lévy processes and applications to insurance risk theory, 2011, arXiv:1101.0445v2 [math.PR].

[23] C. Zhang, R. Wu Total duration of negative surplus for the compound Poisson process that is perturbed by diffusion J. Appl. Probab., 39 (3) (2002), pp. 517–532