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Two-dimensional ruin probability for subexponential claim size

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We analyse the asymptotics of ruin probabilities of two insurance companies (or two branches of the same company) that divide between them both claims and premiums in some specified proportions when the initial reserves of both companies tend to infinity, and generic claim size is subexponential.
Rocznik
Strony
319--335
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Heriot-Watt University, UK
  • Novosibirsk State University, Russia
  • Sobolev Institute of Mathematics, Russia
  • Edinburgh EH14 4AS, Scotland, UK
autor
  • Novosibirsk State University, Russia
  • Lancaster University, UK
  • Lancaster, LA1 4YF, United Kingdom
autor
  • Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
autor
  • Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] S. Asmussen and S. Foss, On exceedance times for some processes with dependent increments, J. Appl. Probab. 51 (2014), pp. 136-151.
  • [2] S. Asmussen and C. Klüppelberg, Large deviations results for subexponential tails, with applications to insurance risk, Stochastic Process. Appl. 64 (1996), pp. 103-125.
  • [3] F. Avram, Z. Palmowski, and M. Pistorius, Exit problem of a two-dimensional risk process from a cone: Exact and asymptotic results, Ann. Appl. Probab. 18 (2008), pp. 2421-2449.
  • [4] F. Avram, Z. Palmowski, and M. Pistorius, A two-dimensional ruin problem on the positive quadrant, Insurance Math. Econom. 42 (2008), pp. 227-234.
  • [5] S. Badila, O. Boxma, J. Resing, and E. M. M. Winands, Queues and risk models with simultaneous arrivals, Adv. in Appl. Probab. 46 (2014), pp. 812-831.
  • [6] Y. Chen, Y. Wang, and K. Wang, Asymptotic results for ruin probability of a two-dimensional renewal risk model, Stoch. Anal. Appl. 31 (2013), pp. 80-91.
  • [7] Y. Chen, Y. Wang, and K. Wang, Uniform asymptotics for the finite-time ruin probabilities of two kinds of nonstandard bidimensional risk models, J. Math. Anal. Appl. 401 (2013), pp. 114-129.
  • [8] Y. Chen, K. Yuen, and K. Ng, Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims, Appl. Stoch. Models Bus. Ind. 27 (3) (2011), pp. 290-300.
  • [9] D. Denisov, S. Foss, and D. Korshunov, Asymptotics of randomly stopped sums in the presence of heavy tails, Bernoulli 16 (4) (2010), pp. 971-994.
  • [10] P. Embrechts, C. Klüppelberg, and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin 1997.
  • [11] S. Foss, D. Korshunov, and S. Zachary, An Introduction to Heavy-Tailed and Subexponential Distributions, Springer, 2013.
  • [12] S. Foss, Z. Palmowski, and S. Zachary, The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk, Ann. Appl. Probab. 3 (2005), pp. 1936-1957.
  • [13] S. Foss and S. Zachary, The maximum on a random time interval of a random walk with long-tailed increments and negative drift, Ann. Appl. Probab. 13 (2003), pp. 37-53.
  • [14] Z. Hu and B. Jiang, On joint ruin probabilities of a two-dimensional risk model with constant interest rate, J. Appl. Probab. 50 (2013), pp. 309-322.
  • [15] T. Jiang, Y. Wang, Y. Chen, and H. Xu, Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model, Insurance Math. Econom. 64 (2015), pp. 45-53.
  • [16] D. G. Konstantinides and J. Li, Asymptotic ruin probabilities for a multidimensional renewal risk model with multivariate regularly varying claims, Insurance Math. Econom. 69 (2016), pp. 38-44.
  • [17] D. Korshunov, On subexponential tails for the maxima of negatively driven compound renewal and Lévy processes, Stochastic Process. Appl. (to appear); available at https://doi.org/10.1016/j.spa.2017.07.013.
  • [18] J. Li, Z. Liu, and Q. Tang, On the ruin probability of a bidimensional perturbed risk model, Insurance Math. Econom. 41 (2007), pp. 185-195.
  • [19] P. M. D. Lieshout and M. Mandjes, Tandem Brownian queues, Math. Methods Oper. Res. 66 (2007), pp. 275-298.
  • [20] D. Lu and B. Zhang, Some asymptotic results of the ruin probabilities in a two-dimensional renewal risk model with some strongly subexponential claims, Statist. Probab. Lett. 114 (2016), pp. 20-29.
  • [21] T. Rolski, H. Schmidli, V. Schmidt, and J. L. Teugles, Stochastic Processes for Insurance and Finance, Wiley, New York 1999.
  • [22] Y. Wang, Z. Cui, K. Wang, and X. Ma, Uniform asymptotics of the finite-time ruin probability for all times, J. Math. Anal. Appl. 390 (2012), pp. 208-223.
  • [23] K. C. Yuen, J. Guo, and X. Wu, On the first time of ruin in the bivariate compound Poisson model, Insurance Math. Econom. 38 (2006), pp. 298-308.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5cbd10bc-f67e-4fe7-a112-3d688c0cdce4
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