Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T10:05:49.728Z Has data issue: false hasContentIssue false
  • English
  • Français

RUIN PROBABILITIES FOR A MULTIDIMENSIONAL RISK MODEL WITH NON-STATIONARY ARRIVALS AND SUBEXPONENTIAL CLAIMS

Published online by Cambridge University Press:  16 March 2021

Ke-Ang Fu Open the ORCID record for Ke-Ang Fu [Opens in a new window]  and
Yang Liu
Ke-Ang Fu
Affiliation:
Department of Statistics, Zhejiang University City College, Hangzhou 310015, China E-mail: [email protected]
Yang Liu
Affiliation:
School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a multidimensional risk model, in which an insurer simultaneously confronts m (m ≥ 2) types of claims sharing a common non-stationary and non-renewal arrival process. Assuming that the claims arrival process satisfies a large deviation principle and the claim-size distributions are heavy-tailed, asymptotic estimates for two common types of ruin probabilities for this multidimensional risk model are obtained. As applications, we give two examples of the non-stationary point process: a Hawkes process and a Cox process with shot noise intensity, and asymptotic ruin probabilities are obtained for these two examples.

Keywords

Cox processHawkes processmultidimensional risk modelnon-stationary arrival processruin probabilitysubexponential class
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 3 , July 2022 , pp. 799 - 811
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albrecher, H. & Asmussen, S. (2006). Ruin probabilities and aggregate claims distributions for shot noise Cox processes. Scandinavian Actuarial Journal 2: 86–110.CrossRefGoogle Scholar
Baltrūnas, A., Daley, D.J., & Klüppelberg, C. (2004). Tail behaviour of the busy period of a GI/GI/1 queuewith subexponential service times. Stochastic Processes and Their Applications 111: 237–258.CrossRefGoogle Scholar
Bordenave, C. & Torrisi, G.L. (2007). Large deviations of Poisson cluster processes. Stochastic Models 23: 593–625.CrossRefGoogle Scholar
Chen, Y., Yuen, K.C., & Ng, K.W. (2011). Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims. Applied Stochastic Models in Business and Industry 27: 290–300.CrossRefGoogle Scholar
Chen, Y., Wang, Y., & Wang, K. (2013). Asymptotic results for ruin probability of a two-dimensional renewal risk model. Stochastic Analysis and Applications 31: 80–91.CrossRefGoogle Scholar
Daley, D.J. & Vere-Jones, D (2003). An introduction to the theory of point processes. vols. I and II, 2nd ed. New York: Springer.Google Scholar
Dembo, A. & Zeitouni, O (1998). Large deviations techniques and applications. New York: Springer.CrossRefGoogle Scholar
Gao, Q. & Yang, X. (2014). Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest. Journal of Mathematical Analysis and Applications 419: 1193–1213.CrossRefGoogle Scholar
Gao, X. & Zhu, L. (2018). Large deviations and applications for Markovian Hawkes processes with a large initial intensity. Bernoulli 24: 2875–2905.CrossRefGoogle Scholar
Hawkes, A.G. (1971). Spectra of some self-exciting and mutually exciting point processes. Biometrika 58: 83–90.CrossRefGoogle Scholar
Konstantinides, D.G. & Li, J. (2016). Asymptotic ruin probabilities for a multidimensional renewal risk model with multivariate regularly varying claims. Insurance Mathematics & Economics 69: 38–44.CrossRefGoogle Scholar
Korshunov, D.A. (2002). Large deviation on probabilities for the maxima of sums of independent summands with a negative mean and a subexponential distribution. Theory of Probability and Its Applications 46: 355–365.CrossRefGoogle Scholar
Leipus, R. & Šiaulys, J. (2007). Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes. Insurance Mathematics & Economics 40: 498–508.CrossRefGoogle Scholar
Li, J. (2018). A revisit to asymptotic ruin probabilities for a bidimensional renewal risk model. Statistics & Probability Letters 140: 23–32.CrossRefGoogle Scholar
Li, J. & Yang, H. (2015). Asymptotic ruin probabilities for a bidimensional renewal risk model with constant interest rate and dependent claims. Journal of Mathematical Analysis and Applications 426: 247–266.CrossRefGoogle Scholar
Li, J., Liu, Z., & Tang, Q. (2007). On the ruin probabilities of a bidimensional perturbed risk model. Insurance Mathematics & Economics 41: 185–195.CrossRefGoogle Scholar
Liu, X., Gao, Q., & Guo, E. (2016). Uniform asymptotics for ruin probability of a two-dimensional dependent renewal risk model. Communications in Statistics – Theory and Methods 45: 6045–6060.CrossRefGoogle Scholar
Lu, D. & Zhang, B. (2016). Some asymptotic results of the ruin probabilities in a two-dimensional renewal risk model with some strongly subexponential claims. Statistics & Probability Letters 114: 20–29.CrossRefGoogle Scholar
Shen, X., Ge, M., & Fu, K.A. (2020). Approximation of the tail probabilities for bidimensional randomly weighted sums with dependent components. Probability in the Engineering and Informational Sciences 34: 112–130.CrossRefGoogle Scholar
Stabile, G. & Torrisi, G.L. (2010). Risk processes with non-stationary Hawkes arrivals. Methodology and Computing in Applied Probability 12: 415–429.CrossRefGoogle Scholar
Yang, H. & Li, J. (2014). Asymptotic finite-time ruin probability for a bidimensional renewal risk model with constant interest force and dependent subexponential claims. Insurance Mathematics & Economics 58: 185–192.CrossRefGoogle Scholar
Yang, Y., Wang, K., Liu, J., & Zhang, Z. (2019). Asymptotics for a bidimensional risk model with two geometric Levy price processes. Journal of Industrial and Management Optimization 15: 481–505.CrossRefGoogle Scholar
Zhu, L. (2013). Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims. Insurance Mathematics & Economics 53: 544–550.CrossRefGoogle Scholar