221
Views
2
CrossRef citations to date
0
Altmetric
Articles

Asymptotics of Parisian ruin of Brownian motion risk model over an infinite-time horizon

Pages 514-528 | Received 27 Mar 2017, Accepted 09 Oct 2017, Published online: 24 Oct 2017

References

  • Adler, R. J. & Taylor, J. E. (2007). Random fields and geometry. Springer monographs in mathematics. New York: Springer.
  • Albrecher, H., Kortschak, D. & Zhou, X. (2012). Pricing of Parisian options for a jump-diffusion model with two-sided jump. Applied Mathematical Finance 19, 97–129.
  • Bai, L., Dȩbicki, K., Hashorva, E. & Ji, L. (2017). Extremes of threshold-dependent Gaussian processes. https://arxiv.org/abs/1701.05387
  • Bai, L., Dȩbicki, K., Hashorva, E. & Luo, L. (2017). On generalised Piterbarg constants. Methodology and Computing in Applied Probability. https://doi.org/10.1007/s11009-016-9537-0
  • Bai, L. & Luo, L. (2017). Parisian ruin of the Brownian motion risk model with constant force of interest. Statistics and Probability Letters 120, 34–44.
  • Chesney, M., Jeanblanc-Picqué, M. \ & Yor, M. (1997). Brownian excursions and Parisian barrier options. Advances in Applied Probability 29, 165–184.
  • Czarna, I. (2016). Parisian ruin probability with a lower ultimate bankrupt barrier. Scandinavian Actuarial Journal 2016, 319–337.
  • Czarna, I. & Palmowski, Z. (2011). Ruin probability with Parisian delay for a spectrally negative Lévy risk process. Journal of Applied Probability 48, 984–1002.
  • Czarna, I. & Palmowski, Z. (2014). Dividend problem with Parisian delay for a spectrally negative Lévy risk process. Journal of Optimization Theory and Applications 161, 239–256.
  • Czarna I., Palmowski Z. & \’{S}wi\c{a}tek P., (2016). Discrete time ruin probability with Parisian delay. Scandinavian Actuarial Journal
  • Dassios, A. & Wu, S. (2009). Parisian ruin with exponential claims. http://stats.lse.ac.uk/angelos/
  • Dassios, A. & Wu, S. (2010). Perturbed brownian motion and its application to Parisian option pricing. Finance and Stochastics 14, 473–494.
  • Dȩbicki, K., Hashorva, E. & Liu, P. (2015). Ruin probabilities and passage times of γ-reflected Gaussian processes with stationary increments. http://arXiv.org/abs/1511.09234
  • D\k{e}bicki, K., Hashorva, E. & Ji, L. (2015). Gaussian risk model with financial constraints. Scandinavian Actuarial Journal 2015(6), 469–481.
  • D\k{e}bicki, K., Hashorva, E. & Ji, L. (2015). Parisian ruin of self-similar Gaussian risk processes. Journal of Applied Probability 52(3), 688–702.
  • D\k{e}bicki, K., Hashorva, E. & Ji, L. (2016). On Parisian ruin over a finite-time horizon. Science China Mathematics 59(3), 557–572.
  • D\k{e}bicki, K. & Mandjes, M. (2003). Exact overflow asymptotics for queues with many Gaussian inputs. Journal of Applied Probability 40(3), 704–720.
  • Emanuel, D. C., Harrison, J. M. & Taylor, A. J. (1975). A diffusion approximation for the ruin function of a risk process with compounding assets. Scandinavian Actuarial Journal 4, 240–247.
  • Embrechts, P., Klüppelberg, C. & Mikosch, T. (1997). Modelling extremal events. Applications of mathematics (New York). Berlin: Springer-Verlag.
  • Harrison, J. M. (1977). Ruin problems with compounding assets. Stochastic Processes and their Applications 5, 67–79.
  • Hashorva, E. & Ji, L. (2015). Approximation of passage times of γ-reflected processes with fBm input. Journal of Applied Probability 51(3), 713–726.
  • Hashorva, E. & Ji, L. (2015). Piterbarg theorems for chi-processes with trend. Extremes 18(1), 37–64.
  • He, X. & Hu, Y. (2007). Ruin probability for the integrated Gaussian process with force of interest. Journal of Applied Probability 44, 685–694.
  • Hüsler, J. & Piterbarg, V. I. (2008). A limit theorem for the time of ruin in a Gaussian ruin problem. Stochastic Processes and their Applications 118(11), 2014–2021.
  • Leoffen, R., Czarna, I. & Palmowski, Z. (2013). Parisian ruin probability for spectrally negative Lévy processes. Bernoulli 19, 599–609.
  • Li, B., Tang, Q., Wang, L. & Zhou, X. (2014). Liquidation risk in the presence of Chapters 7 and 11 of the US bankruptcy code. Journal of Financial Engineering 01(3), 1450023.
  • Makarov, R. N. (2016). Modelling liquidation risk with occupation times. International Journal of Financial Engineering 03(04), 1650028.
  • Meyer, P. A. (1966). Probability and potentials. Waltham, MA: Blaisdell.
  • Piterbarg, V. I. (1996). Asymptotic methods in the theory of Gaussian processes and fields, Vol. 148, Translations of mathematical monographs. Providence, RI: American Mathematical Society.
  • Rolski, T., Schmidli, H., Schmidt, V. & Teugels, J. (2009). Stochastic processes for insurance and finance. Wiley Series in Probability and Statistics. Chichester: Wiley.

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.