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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 1, Pages 188–194 (Mi tvp310)  

This article is cited in 16 scientific papers (total in 16 papers)

Short Communications

Ruin probabilities for Lévy processes with mixed-exponential negative jumps

É. Mordecki

Facultad de Ciencias, Centro de Matemática

Abstract: We give a closed form of the ruin probability for Lévy processes, possible killed at a constant rate, with arbitrary, positive, and mixed exponentially negative jumps.

Keywords: ruin probability, closed form, Lévy process, mixed-exponential distributions.

DOI: https://doi.org/10.4213/tvp310

Full text: PDF file (689 kB)
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English version:
Theory of Probability and its Applications, 2004, 48:1, 170–176

Bibliographic databases:

Received: 18.11.1999
Language:

Citation: É. Mordecki, “Ruin probabilities for Lévy processes with mixed-exponential negative jumps”, Teor. Veroyatnost. i Primenen., 48:1 (2003), 188–194; Theory Probab. Appl., 48:1 (2004), 170–176

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Asmussen S., Avram F., Pistorius M.R., “Russian and American put options under exponential phase-type Lévy models”, Stochastic Process. Appl., 109:1 (2004), 79–111  crossref  mathscinet  zmath  isi  scopus
    2. A. N. Borodin, “Distributions of functionals of diffusions with jumps”, J. Math. Sci. (N. Y.), 139:3 (2006), 6510–6519  mathnet  crossref  mathscinet  zmath
    3. A. N. Borodin, “Distributions of functionals of diffusions with jumps”, J. Math. Sci. (N. Y.), 145:2 (2007), 4843–4855  mathnet  crossref  mathscinet  zmath
    4. A. N. Borodin, “On distributions of passage times of Brownian motion with jumps”, J. Math. Sci. (N. Y.), 152:6 (2008), 853–861  mathnet  crossref
    5. A. N. Borodin, “Distributions of functionals of bridges of diffusions with jumps”, J. Math. Sci. (N. Y.), 147:4 (2007), 6864–6872  mathnet  crossref  mathscinet  zmath
    6. Lewis A.L., Mordecki E., “Wiener–Hopf factorization for Lévy processes having positive jumps with rational transforms”, J. Appl. Probab., 45:1 (2008), 118–134  crossref  mathscinet  zmath  isi  scopus
    7. A. N. Borodin, “On first exit time from an interval for diffusions with jumps”, J. Math. Sci. (N. Y.), 163:4 (2010), 352–362  mathnet  crossref
    8. A. N. Borodin, “Distributions of the location of the maximum and minimum for diffusions with jumps”, J. Math. Sci. (N. Y.), 167:4 (2010), 474–485  mathnet  crossref
    9. Christensen S., Irle A., “A note on pasting conditions for the American perpetual optimal stopping problem”, Statist. Probab. Lett., 79:3 (2009), 349–353  crossref  mathscinet  zmath  isi  elib  scopus
    10. A. N. Borodin, “Distributions of functionals of diffusions with jumps connected with the location of the maximum or minimum”, J. Math. Sci. (N. Y.), 176:2 (2011), 146–161  mathnet  crossref
    11. A. N. Borodin, “Joint distributions of the infimum, the supremum and the end of Brownian motion with jumps”, J. Math. Sci. (N. Y.), 188:6 (2013), 677–685  mathnet  crossref  mathscinet
    12. Jacobsen M., “Exit Times for a Class of Random Walks: Exact Distribution Results”, J. Appl. Probab., 48A:SI (2011), 51–63  crossref  mathscinet  zmath  isi  scopus
    13. D. Gusak, Ie. Karnaukh, “The unified form of Pollaczek–Khinchine formula for Lévy processes with matrix-exponential negative jumps”, Theory Stoch. Process., 18(34):2 (2012), 15–23  mathnet  mathscinet
    14. A. N. Borodin, “Distributions of functionals of diffusions with jumps stopped at random moments”, J. Math. Sci. (N. Y.), 206:2 (2015), 115–126  mathnet  crossref
    15. Mordecki E., Mishura Yu., “Optimal Stopping for Lévy Processes with One-Sided Solutions”, SIAM J. Control Optim., 54:5 (2016), 2553–2567  crossref  mathscinet  zmath  isi  elib  scopus
    16. Korshunov D., “On Subexponential Tails For the Maxima of Negatively Driven Compound Renewal and Levy Processes”, Stoch. Process. Their Appl., 128:4 (2018), 1316–1332  crossref  mathscinet  zmath  isi  scopus
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