View More View Less
  • 1 University of Zagreb, Zagreb, Croatia
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00


We study the discrete time risk process modelled by the skip-free random walk and derive results connected to the ruin probability and crossing a fixed level for this type of process. We use the method relying on the classical ballot theorems to derive the results for crossing a fixed level and compare them to the results known for the continuous time version of the risk process. We generalize this model by adding a perturbation and, still relying on the skip-free structure of that process, we generalize the previous results on crossing the fixed level for the generalized discrete time risk process. We further derive the famous Pollaczek-Khinchine type formula for this generalized process, using the decomposition of the supremum of the dual process at some special instants of time.

  • [1]

    Addario-Berry, L. and Reed, B. A., Ballot theorems, old and new, Horizons of Combinatorics, Bolyai Society Mathematical Studies 17 (2008), 935.

    • Search Google Scholar
    • Export Citation
  • [2]

    Dwass, M., A fluctuation theorem for cyclic random variables, Ann.Math.Statist., 33 (4) (1962), 14501454.

  • [3]

    Feller, W., An introduction to probability theory and its applications, Vol II, 2nd edition, Wiley, 1971.

  • [4]

    Huzak, M., Perman, M., Šikić, H. and Vondraček, Z., Ruin probabilities and decompositions for general perturbed risk processes, Ann. Appl. Probab., 14, (2004), 13781397.

    • Search Google Scholar
    • Export Citation
  • [5]

    Huzak, M., Perman, M., Šikić, H. and Vondraček, Z., Ruin probabilities for competing claim processes, J. Appl.Probab., 41 (2004), 679690.

    • Search Google Scholar
    • Export Citation
  • [6]

    Lambert, A., Some aspects of discrete branching processes, Université Paris VI Pierre et Marie Curie, France (2010)

    • Search Google Scholar
    • Export Citation
  • [7]

    Takács, L., On combinatorial methods in the theory of stochastic processes, Krieger, Huntington, NY, 1977.

  • [8]

    Tuđen, I. G., Distribution of suprema for generalized risk processes, Stochastic Models, 35 (1), (2019), 3350.

  • [9]

    Tuđen, I. G. and Vondraček, Z., A distributional equality for suprema of spectrally positive Lévy processes, Journal of the theoretical probability, 29 (3) (2016), 826842

    • Search Google Scholar
    • Export Citation

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE


  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • The ISI Alerting Services


Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333