基于相依风险模型下的阈值分红策略的若干问题研究
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摘要
首先介绍带有阈值分红的索赔额相依风险模型,然后给出Gerber-Shiu折现罚金函数满足的积分微分方程及其解的分析,最后给出红利折现期望满足的齐次积分微分方程.
At first,a threshold dividend strategy in a risk model with interclaim-dependent claim sizes is introduced.Then,an integro-differeential equation for the Gerber-Shiu discounted penalty function in this risk model is derived,and the solution to the Gerber-Shiu discounted penalty function is analyzed.Finally,an homogeneous integro-differential equation for the expected discounted dividend payments before ruin is derived.
At first,a threshold dividend strategy in a risk model with interclaim-dependent claim sizes is introduced.Then,an integro-differeential equation for the Gerber-Shiu discounted penalty function in this risk model is derived,and the solution to the Gerber-Shiu discounted penalty function is analyzed.Finally,an homogeneous integro-differential equation for the expected discounted dividend payments before ruin is derived.
引文
[1]Albrecher,H.,Claramunt,M.M.,Marmol,M.On a distribution of dividend payments in a Sparre Andersen model with generalized Erlang(n) interclaim times[J].Insurance:Mathematics and Economics,37(2005):324-334.
[2]Albrecher,H.,Boxma,O.J.A ruin model with dependence between claim sizes and claim intervals[J].Insurance:Mathematics and Economics,35(2004):245-254.
[3]Asmussen,S.,Taksar,M.Controlled diffusion models for optimal dividend pay-out[J].Insurance:Mathematics and Economics 20(1997):1-15.
[4]Boudreault,M.Cossette,H.,Landriault,D.,Marceau,E.On a risk model with depen-dence between interclaim arrivals and claim sizes[J].Scand.Actuar.J.,3(2006):265-285.
[5]David Landriault.Constant dividend barrier in a risk model with interclaim-dependent claim sizes[J].Insurance:Mathematics and Economics,42(2008):31-38.
[6]Dickson,D.C.M.,Hipp,C.On the time to ruin for Erlang(2) risk process]J].Insurance:Mathematics and Economics,29(2001):333-344.
[7]David Landriault,Gordon Willmot.On the Gerber-Shin discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution[J].Insurance:Mathmatics and Economics,42(2008):600-608.
[8]Gerber,H.U.,Shiu,E.S:W.The time value of ruin in a Sparre Andersen risk model[J].North American Actuarial,9(2005):49-69.
[9]Gerber,H.U.,Shiu,E.S.W.On Optimal Dividend Strategies in the Compound Poisson Model[J].North American Actuarial,10(2006):76-93.
[10]Gerber,H.U.,Shiu,E.S.W.Optimal dividend strategies in a Cramer-Lundberg model with capital injections[J].Insurance:Mathmatics and Economics,43(2008):270-278.
[11]Gerber,H.U.,Shiu,E.S.W.On the time value of ruin[J].North American Actuarial,1(1998):48-78.
[12]Heli Gao,Chuancun Yin.The perturbed Sparre Andersen model with a threshold dividend strategy[J].Journal of Computational and Applied Mathematics,(2007).
[13]Hu Yang,Zhimin Zhang.Gerber-Shin discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy[J].Insurance:Mathematics and Economics,42(2008):984-991.
[14]Jun Cai,David C.M.,Dickson.On the expected discounted penalty function at ruin of a surplus process with interest[J].Insurance:Mathematics and Economics,30(2002):389-404.
[15]Kristina P.Pavlova,Gordon E.Willmot.The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function[J].Insurance:Mathematics and Economics,35(2004):267-277.
[16]Lin,X.s.,Willmot,G.E.,Drekic,S.The classical risk model with a constant dividend barrier:Analysis of the Gerber-Shiu discounted penalty function[J].Insurance:Mathematics and Economics,33(2003):551-566.
[17]Ning Wan Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion[J].Insurance:Mathematics and Economics,40(2007):509-523.
[18]S.Li,J.Garrido.On a class of renewal risk models with a constant dividend barrier [J].Insurance:Mathematics and Economics,35(2004):691-701.
[19]X.Sheldon Lin,Kristina P.Pavlova.The compound Poisson risk model with a threshold dividend strategy[J].Insurance:Mathematics and Economics,38(2006):57-80.
[20]X.W.Zhou.On a classical risk model with a constant dividend barrier[J].North American Actuarial,9(2005):95-108.
[2]Albrecher,H.,Boxma,O.J.A ruin model with dependence between claim sizes and claim intervals[J].Insurance:Mathematics and Economics,35(2004):245-254.
[3]Asmussen,S.,Taksar,M.Controlled diffusion models for optimal dividend pay-out[J].Insurance:Mathematics and Economics 20(1997):1-15.
[4]Boudreault,M.Cossette,H.,Landriault,D.,Marceau,E.On a risk model with depen-dence between interclaim arrivals and claim sizes[J].Scand.Actuar.J.,3(2006):265-285.
[5]David Landriault.Constant dividend barrier in a risk model with interclaim-dependent claim sizes[J].Insurance:Mathematics and Economics,42(2008):31-38.
[6]Dickson,D.C.M.,Hipp,C.On the time to ruin for Erlang(2) risk process]J].Insurance:Mathematics and Economics,29(2001):333-344.
[7]David Landriault,Gordon Willmot.On the Gerber-Shin discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution[J].Insurance:Mathmatics and Economics,42(2008):600-608.
[8]Gerber,H.U.,Shiu,E.S:W.The time value of ruin in a Sparre Andersen risk model[J].North American Actuarial,9(2005):49-69.
[9]Gerber,H.U.,Shiu,E.S.W.On Optimal Dividend Strategies in the Compound Poisson Model[J].North American Actuarial,10(2006):76-93.
[10]Gerber,H.U.,Shiu,E.S.W.Optimal dividend strategies in a Cramer-Lundberg model with capital injections[J].Insurance:Mathmatics and Economics,43(2008):270-278.
[11]Gerber,H.U.,Shiu,E.S.W.On the time value of ruin[J].North American Actuarial,1(1998):48-78.
[12]Heli Gao,Chuancun Yin.The perturbed Sparre Andersen model with a threshold dividend strategy[J].Journal of Computational and Applied Mathematics,(2007).
[13]Hu Yang,Zhimin Zhang.Gerber-Shin discounted penalty function in a Sparre Andersen model with multi-layer dividend strategy[J].Insurance:Mathematics and Economics,42(2008):984-991.
[14]Jun Cai,David C.M.,Dickson.On the expected discounted penalty function at ruin of a surplus process with interest[J].Insurance:Mathematics and Economics,30(2002):389-404.
[15]Kristina P.Pavlova,Gordon E.Willmot.The discrete stationary renewal risk model and the Gerber-Shiu discounted penalty function[J].Insurance:Mathematics and Economics,35(2004):267-277.
[16]Lin,X.s.,Willmot,G.E.,Drekic,S.The classical risk model with a constant dividend barrier:Analysis of the Gerber-Shiu discounted penalty function[J].Insurance:Mathematics and Economics,33(2003):551-566.
[17]Ning Wan Dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion[J].Insurance:Mathematics and Economics,40(2007):509-523.
[18]S.Li,J.Garrido.On a class of renewal risk models with a constant dividend barrier [J].Insurance:Mathematics and Economics,35(2004):691-701.
[19]X.Sheldon Lin,Kristina P.Pavlova.The compound Poisson risk model with a threshold dividend strategy[J].Insurance:Mathematics and Economics,38(2006):57-80.
[20]X.W.Zhou.On a classical risk model with a constant dividend barrier[J].North American Actuarial,9(2005):95-108.