EXACT AND ASYMPTOTIC RESULTS FOR INSURANCE RISK MODELS WITH SURPLUS-DEPENDENT PREMIUMS

被引：27

作者：

Albrecher, Hansjoerg ^{[1
,2
]}

Constantinescu, Corina ^{[3
]}

Palmowski, Zbigniew ^{[4
]}

Regensburger, Georg ^{[5
]}

Rosenkranz, Markus ^{[6
]}

机构：

[1] Univ Lausanne, Dept Actuarial Sci, Fac Business & Econ, CH-1015 Lausanne, Switzerland

[2] Swiss Finance Inst, CH-8006 Zurich, Switzerland

[3] Univ Liverpool, Dept Math Sci, Inst Financial & Actuarial Math, Liverpool L69 7ZL, Merseyside, England

[4] Univ Wroclaw, Math Inst, PL-50384 Wroclaw, Poland

[5] INRIA Saclay Ile France, Project DISCO, L2S, Supelec, F-91192 Gif Sur Yvette, France

[6] Univ Kent, Sch Math Stat & Actuarial Sci, Canterbury CT2 7NF, Kent, England

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 2013年 / 73卷 / 01期

基金：

瑞士国家科学基金会; 奥地利科学基金会;

关键词：

renewal risk models; surplus dependent premiums; boundary value problems; Green's operators; asymptotic expansions; BOUNDARY-PROBLEMS; FACTORIZATION;

D O I：

10.1137/110852000

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we develop a symbolic technique to obtain asymptotic expressions for ruin probabilities and discounted penalty functions in renewal insurance risk models when the premium income depends on the present surplus of the insurance portfolio. The analysis is based on boundary problems for linear ordinary differential equations with variable coefficients. The algebraic structure of the Green's operators allows us to develop an intuitive way of tackling the asymptotic behavior of the solutions, leading to exponential-type expansions and Cramer-type asymptotics. Furthermore, we obtain closed-form solutions for more specific cases of premium functions in the compound Poisson risk model.

引用

页码：47 / 66

页数：20

共 24 条

[1]

Abramowitz M., 2013, Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables, V(eds)

[2] On a gamma series expansion for the time-dependent probability of collective ruin [J].

Albrecher, H ;

Teugels, JL ;

Tichy, RF .

INSURANCE MATHEMATICS & ECONOMICS, 2001, 29 (03) :345-355

[3] An algebraic operator approach to the analysis of Gerber-Shiu functions [J].

Albrecher, Hansjoerg ;

Constantinescu, Corina ;

Pirsic, Gottlieb ;

Regensburger, Georg ;

Rosenkranz, Markus .

INSURANCE MATHEMATICS & ECONOMICS, 2010, 46 (01) :42-51

[4]

[Anonymous], 1944, Ordinary Differential Equations

[5]

Asmussen S., 2010, ADV SER STAT SCI APP, V14

[6]

Coddington E. A., 1955, THEORY ORDINARY DIFF

[7]

Constantinescu C., 2011, MARTINGALES RENEWAL

[8]

Fedoryuk M.V., 1993, Asymptotic Analysis: Linear Ordinary Differential Equations

[9]

Gerber HU., 1998, North Amer-ican Actuarial Journal, V2, P48, DOI [10.1080/10920277.1998.10595671, DOI 10.1080/10920277.1998.10595671]

[10]

Grobner W., 1966, MATRIZENRECHNUNG

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