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

被引：3

作者：

Fu, Ke-Ang ^{[1
]}

Liu, Yang ^{[2
]}

机构：

[1] Zhejiang Univ City Coll, Dept Stat, Hangzhou 310015, Peoples R China

[2] Zhejiang Gongshang Univ, Sch Stat & Math, Hangzhou 310018, Peoples R China

来源：

PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES | 2022年 / 36卷 / 03期

关键词：

Cox process; Hawkes process; multidimensional risk model; non-stationary arrival process; ruin probability; subexponential class; LARGE DEVIATIONS; ASYMPTOTICS; BEHAVIOR; FORCE; SUMS;

D O I：

10.1017/S0269964821000085

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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.

引用

页码：799 / 811

页数：13

共 23 条

[1]

Albrecher H., 2006, Scand. Actuar. J., V2006, P86

[2] Tail behaviour of the busy period of a GI/GI/1 queue with subexponential service times [J].

Baltrunas, A ;

Daley, DJ ;

Klüppelberg, C .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2004, 111 (02) :237-258

[3] Large deviations of poisson cluster processes [J].

Bordenave, Charles ;

Torrisi, Giovanni Luea .

STOCHASTIC MODELS, 2007, 23 (04) :593-625

[4] Asymptotic Results for Ruin Probability of a Two-Dimensional Renewal Risk Model [J].

Chen, Yang ;

Wang, Yuebao ;

Wang, Kaiyong .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2013, 31 (01) :80-91

[5] Asymptotics for the ruin probabilities of a two-dimensional renewal risk model with heavy-tailed claims [J].

Chen, Yiqing ;

Yuen, Kam C. ;

Ng, Kai W. .

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, 2011, 27 (03) :290-300

[6]

Daley D.J., 2003, Elementary theory and methods, VI

[7]

DEMBO A., 1998, Applications of Mathematics, V2nd

[8] Asymptotic ruin probabilities in a generalized bidimensional risk model perturbed by diffusion with constant force of interest [J].

Gao, Qingwu ;

Yang, Xiuzhu .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 419 (02) :1193-1213

[9] Large deviations and applications for Markovian Hawkes processes with a large initial intensity [J].

Gao, Xuefeng ;

Zhu, Lingjiong .

BERNOULLI, 2018, 24 (4A) :2875-2905

[10]

HAWKES AG, 1971, BIOMETRIKA, V58, P83, DOI 10.1093/biomet/58.1.83

← 1 2 3 →