Approximations of the ruin probability in a discrete time risk model

被引：7

作者：

Santana, David J. ^{[1
]}

Rincon, Luis ^{[2
]}

机构：

[1] UJAT, Div Acad Ciencias Basicas, Villahermosa, Mexico

[2] Univ Nacl Autonoma Mexico, Dept Matemat, Fac Ciencias, Mexico City, DF, Mexico

来源：

MODERN STOCHASTICS-THEORY AND APPLICATIONS | 2020年 / 7卷 / 03期

关键词：

Ruin probability; risk process; MIXTURES;

D O I：

10.15559/20-VMSTA158

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Based on a discrete version of the Pollaczeck-Khinchine formula, a general method to calculate the ultimate ruin probability in the Gerber-Dickson risk model is provided when claims follow a negative binomial mixture distribution. The result is then extended for claims with a mixed Poisson distribution. The formula obtained allows for some approximation procedures. Several examples are provided along with the numerical evidence of the accuracy of the approximations.

引用

页码：221 / 243

页数：23

共 19 条

[11] A review of discrete-time risk models [J].

Li, Shuanming ;

Lu, Yi ;

Garrido, Jose .

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2009, 103 (02) :321-337

[12] POISSON MIXTURES AND QUASI-INFINITE DIVISIBILITY OF DISTRIBUTIONS [J].

PURI, PS ;

GOLDIE, CM .

JOURNAL OF APPLIED PROBABILITY, 1979, 16 (01) :138-153

[13] Approximation of the Ultimate Ruin Probability in the Classical Risk Model Using Erlang Mixtures [J].

Santana, David J. ;

Gonzalez-Hernandez, Juan ;

Rincon, Luis .

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY, 2017, 19 (03) :775-798

[14]

Shiu E.S.W., 1989, ASTIN Bull, V19, P179, DOI DOI 10.2143/AST.19.2.2014907

[15]

Steutel F.W., 1997, Stochastic Models, V13, P271

[16]

Willmot G.E., 1993, Scandinavian Actuarial Journal, V18, P114

[17] ON THE CLASS OF ERLANG MIXTURES WITH RISK THEORETIC APPLICATIONS [J].

Willmot, Gordon ;

Woo, Jae-Kyung .

NORTH AMERICAN ACTUARIAL JOURNAL, 2007, 11 (02) :99-115

[18] Risk modelling with the mixed Erlang distribution [J].

Willmot, Gordon E. ;

Lin, X. Sheldon .

APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, 2011, 27 (01) :8-22

[19]

2012, SMART NAN SENS APPL, P1

← 1 2 →