Cai, Chunhao; Li, Bo Occupation times of intervals until last passage times for spectrally negative Lévy processes. (English) Zbl 1434.60128 J. Theor. Probab. 31, No. 4, 2194-2215 (2018). “In this paper, (the authors) derive the Laplace transform of occupation times of intervals until last passage times for spectrally negative Lévy processes.” They investigate the last passage times before an independent exponential variable. Questions of this kind are motivated by earlier work of E. J. Baurdoux [J. Appl. Probab. 46, No. 2, 542–558 (2009; Zbl 1170.60020)]. “By a dual argument, explicit formulas are obtained and expressed as a modified version of the analytical identities introduced in [R. L. Loeffen et al., Stochastic Processes Appl. 124, No. 3, 1408–1435 (2014; Zbl 1287.60062)]. As an application (of the obtained results), a corridor option and an Omega risk model are studied.” Reviewer: Alexander Schnurr (Siegen) Cited in 1 ReviewCited in 6 Documents MSC: 60G51 Processes with independent increments; Lévy processes 60J55 Local time and additive functionals 60J76 Jump processes on general state spaces 91G20 Derivative securities (option pricing, hedging, etc.) 91G05 Actuarial mathematics Keywords:occupation times; spectrally negative Lévy process; last passage times; scale functions; Laplace transform; risk theory Citations:Zbl 1170.60020; Zbl 1287.60062 PDFBibTeX XMLCite \textit{C. Cai} and \textit{B. Li}, J. Theor. Probab. 31, No. 4, 2194--2215 (2018; Zbl 1434.60128) Full Text: DOI arXiv References: [1] Albrecher, H.; Gerber, HU; Shiu, ESW, The optimal dividend barrier in the gamma-omega model, Eur. Actuar. J., 1, 43-55, (2011) · Zbl 1219.91062 [2] Baurdoux, EJ, Last exit before an exponential time for spectrally negative Lévy processes, J. Appl. Probab., 46, 542-558, (2009) · Zbl 1170.60020 [3] Bertoin, J.: Lévy processes. In: Cambridge Tracts in Mathematics (1996) [4] Gerber, HU, When does the surplus reach a given target?, Insur. Math. Econ., 9, 115-119, (1990) · Zbl 0731.62153 [5] Gerber, HU; Shiu, ESW; Yang, H., The omega model: from bankruptcy to occupation times in the red, Eur. Actuar. J., 2, 259-272, (2012) · Zbl 1256.91057 [6] Guérin, H., Renaud, J.F.: Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view (2014). arXiv:1406.3130 [7] Ivanovs, J.; Palmowski, Z., Occupation densities in solving exit problems for markov additive processes and their reflections, Stoch. Process. Appl., 122, 3342-3360, (2012) · Zbl 1267.60087 [8] Kyprianou, A.E.: Fluctuations of Lévy Processes with Applications. Springer, Berlin (2014). doi:10.1007/978-3-642-37632-0 · Zbl 1384.60003 [9] Kyprianou, AE; Pardo, JC; Pérez, JL, Occupation times of refracted Lévy processes, J. Theor. Probab., 27, 1292-1315, (2014) · Zbl 1306.60049 [10] Landriault, David; Renaud, Jean-François; Zhou, Xiaowen, Occupation times of spectrally negative Lévy processes with applications, Stochastic Processes and their Applications, 121, 2629-2641, (2011) · Zbl 1227.60061 [11] Li, B.; Zhou, X., The joint Laplace transforms for diffusion occupation times, Adv. Appl. Probab., 45, 1049-1067, (2013) · Zbl 1370.60136 [12] Lia, Y., Yin, C., Zhou, X.: On the last exit times for spectrally negative Lévy processes (2016). arXiv:1606.04622 [math.PR] [13] Loeffen, RL; Renaud, JF; Zhou, X., Occupation times of intervals until first passage times for spectrally negative Lévy processes, Stoch. Process. Appl., 124, 1408-1435, (2014) · Zbl 1287.60062 [14] Nok Chiu, S.; Yin, C., Passage times for a spectrally negative Lévy process with applications to risk theory, Bernoulli, 11, 511-522, (2005) · Zbl 1076.60038 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.