280
Views
10
CrossRef citations to date
0
Altmetric
Articles

Discrete time ruin probability with Parisian delay

, &
Pages 854-869 | Received 14 Jul 2015, Accepted 10 Nov 2016, Published online: 07 Dec 2016

References

  • Albrecher, H., Kortschak, D. & Zhou, X. (2012). Pricing of Parisian options for a jump-diffusion model with two-sided jumps. Applied Mathematical Finance 19(2), 97–129.
  • Alili, L., Chaumont, L. & Doney, R. (2005). On a fluctuation identity for random walks and Lévy processes. Bulletin of the London Mathematical Society 37, 141–148.
  • Asmussen, S. (2003). Applied probability and queues. New York: Springer.
  • Asmussen, S. & Albrecher, H. (2010). Ruin probabilities. Singapore: World Scientific.
  • Baurdoux, E. J., Pardo, J. C., Pérez, J. L. & Renaud, J.-F. (2016). Gerber–Shiu functionals at Parisian ruin for Lévy insurance risk processes. Advances in Applied Probability 53, 572–584.
  • Bertoin, J. (1996). Lévy processes. Cambridge: Cambridge University Press.
  • Bertoin, J. & Doney, R. (1996). Some Asymptotic results for transient random walks. Advances in Applied Probability 28(1), 207–226.
  • Cheng, S., Gerber, H. U. & Shiu, E. S. W. (2000). Discounted probabilities and ruin theory in the compound binomial model. Insurance: Mathematics and Economics 26, 239–250.
  • Chesney, M., Jeanblanc-Picqué, M. & Yor, M. (1997). Brownian excursions and Parisian barrier options. Advances in Applied Probability 29(1), 165–184.
  • Cossette, H., Landriault, D. & Marceau, E. (2003). Ruin probabilities in the compound Markov binomial model. Scandinavian Actuarial Journal 4, 301–323.
  • Cossette, H., Landriault, D. & Marceau, E. (2004). Compound binomial risk model in a Markovian environment. Insurance: Mathematics and Economics 35, 425–443.
  • Cossette, H., Landriault, D. & Marceau, E. (2006). Ruin probabilities in the discrete time renewal risk model. Insurance: Mathematics and Economics 38, 309–323.
  • Czarna, I. & Palmowski, Z. (2011). Ruin probability with Parisian delay for a spectrally negative Lévy risk process. Journal of Applied Probability 48(4), 984–1002.
  • Dassios, A. & Wu, S. (2009a). Parisian ruin with exponential claims. Submitted for publication. http://stats.lse.ac.uk/angelos/
  • Dassios, A. & Wu, S. (2009b). Ruin probabilities of the Parisian type for small claims. Submitted for publication. http://stats.lse.ac.uk/angelos/
  • De Vylder, F. E. & Goovaerts, M. J. (1988). Recursive calculation of finite-time ruin probabilities. Insurance: Mathematics and Economics 7, 1–7.
  • Dickson, D. C. M. (1992). On the distribution of surplus prior to ruin. Insurance: Mathematics and Economics 11, 191–207.
  • Dickson, D. C. M. (1994). Some comments on the compound binomial model. ASTIN Bulletin 24, 33–45.
  • Dickson, D. C. M. (2005). Insurance risk and ruin. Cambridge: Cambridge University Press.
  • Dickson, D. C. M., dos Reis, E. A. D. & Waters, H. R. (1995). Some stable algorithms in ruin theory and their applications. ASTIN Bulletin 25, 153–175.
  • Dickson, D. C. M. & Hipp, C. (2001). On the time to ruin for Erlang(2) risk process. Insurance: Mathematics and Economics 29, 333–344.
  • Dickson, D. C. M. & Waters, H. R. (1991). Recursive calculation of survival probabilities. ASTIN Bulletin 21, 199–221.
  • dos Reis, A. E. (1993). The compound binomial model revisited. Manuscript. Available at http://www.actuaries.org/ASTIN/Colloquia/Bergen/EgidiodosReis.pdf
  • Feller, W. (1966). An introduction to probability theory and its applications, Vol. II. New York: Wiley.
  • Foss, S., Korshunov, D. & Zachary, S. (2011). An introduction to heavy-tailed and subexponential distributions. New York: Springer.
  • Gerber, E. (1988). Mathematical fun with the compound binomial process. ASTIN Bulletin 18, 161–168.
  • Gerber, H. U. & Shiu, E. S. W. (1998). On the time value of ruin. North American Actuarial Journal 2(1), 48–78.
  • Gerber, H. U. & Shiu, E. S. W. (2005). The time value of ruin in a Sparre Andersen model. North American Actuarial Journal 9(2), 49–69.
  • Klüppelberg, C. & Kyprianou, A. (2006). On extreme ruinous behaviour of Lévy insurance risk process. Journal of Applied Probability 43(2), 594–598.
  • Landriault, D. (2008). On a generalization of the expected discounted penalty function in a discrete-time insurance risk model. Applied Stochastic Models in Business and Industry 24, 525–539.
  • Landriault, D., Renaud, J. F. & Zhou, X. (2014). Insurance risk models with Parisian implementation delays. Methodology and Computing in Applied Probability 16(3), 583–607.
  • Lefévre, C. & Loisel, S. (2008). On finite-time ruin probabilities for classisal risk models. Scandinavian Actuarial Journal 1, 41–60.
  • Li, S. (2005). On a class of discrete-time renewal risk models. Scandinavian Actuarial Journal 4, 241–260.
  • Li, S. (2005). Distributions of the surplus before ruin, the deficit at ruin and the claim causing ruin in a class of discrete time risk models. Scandinavian Actuarial Journal 4, 271–284.
  • Li, S. & Garrido, J., On the time value of ruin in the discrete time risk model. Working paper 02–18, Business Economics. Madrid: University Carlos III of Madrid, 2002.
  • Li, S. & Garrido, J. (2004). On ruin for Erlang(n) risk process. Insurance: Mathematics and Economics 34, 391–408.
  • Li, S. & Garrido, J. (2005). On a general class of renewal risk process: analysis of the Gerber-Shiu penalty function. Advances in Applied Probability 37, 836–856.
  • Li, S., Lu, Y. & Garrido, J. (2009). A review of discrete-time risk models. R ACSAM - Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales. Serie A. Matematicas 103(2), 321–337.
  • Lin, X. S. & Willmot, G. E. (1999). Analysis of a defective renewal arising in ruin theory. Insurance: Mathematics and Economics 25, 63–84.
  • Lin, X. S. & Willmot, G. E. (2000). The moments of the time of ruin, the surplus before ruin and the deficit at ruin. Insurance: Mathematics and Economics 27, 19–44.
  • Liu, S. X. & Guo, J. Y. (2006). Discrete risk model revisited. Methodology and Computing in Applied Probability 8(2), 303–313.
  • Loeffen, R., Czarna, I. & Palmowski, Z. (2013). Parisian ruin probability for spectrally negative Lévy processes. Bernoulli 19(2), 599–609.
  • Michel, R. (1989). Representation of a time-discrete probability of eventual ruin. Insurance: Mathematics and Economics 8, 149–152.
  • Pavlova, K. & Willmot, G. E. (2004). The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function. Insurance: Mathematics and Economics 35, 267–277.
  • Rolski, T., Schmidli, H., Schmidt, V. & Teugels, J. L. (1999). Stochastic processes for insurance and finance. New York: John Wiley and Sons.
  • Shiu, E. (1989). The probability of eventual ruin in the compound binomial model. ASTIN Bulletin 19, 179–190.
  • Tang, Q. (2006). On convolution equivalence with applications. Bernoulli 12(3), 535–549.
  • Tang, Q. & Tsitsiashvili, G. (2003). Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stochastic Processes and Their Applications 108(2), 299–325.
  • Willmot, G. E. (1993). Ruin probabilities in the compound binomial model. Insurance: Mathematics and Economics 12, 133–142.
  • Willmot, G. E. (1999). A Laplace transform representation in a class of renewal queueing and risk processes. Journal of Applied Probability 36, 570–584.
  • Willmot, G. E. & Lin, X. S. (2001). Lundberg approximations for compound distributions with insurance applications. Lecture notes in statistics. New York: Springer-Verlag.
  • Wu, X. & Li, S. (2009). On the Gerber–Shiu function in a discrete time renewal risk model with general inter-claim times. Scandinavian Actuarial Journal 4, 281–294.
  • Yang, H., Zhang, Z. & Lan, C. (2009). Ruin problems in a discrete Markov risk model. Statistics and Probability Letters 79, 21–28.
  • Yuen, K. C. & Guo, J. (2001). Ruin probabilities for time-correlated claims in the compound binomial model. Insurance: Mathematics and Economics 29, 47–57.
  • Yuen, K. C. & Guo, J. (2006). Some results on the compound binomial model. Scandinavian Actuarial Journal 3, 129–140.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.