【摘要】：在隨機(jī)過(guò)程及其應(yīng)用的領(lǐng)域,關(guān)于保險(xiǎn)風(fēng)險(xiǎn)模型的文章是數(shù)不勝數(shù),人們也不再僅僅滿足于對(duì)古典風(fēng)險(xiǎn)模型的研究.到目前為止,更新風(fēng)險(xiǎn)模型,帶擾動(dòng)的風(fēng)險(xiǎn)模型,索賠過(guò)程相依的模型,保費(fèi)隨機(jī)化的模型,對(duì)偶模型等都得到了廣泛地研究.這篇論文討論一種新型的相依模型,即在保費(fèi)隨機(jī)化模型的基礎(chǔ)上對(duì)于保費(fèi)收取過(guò)程做進(jìn)步推廣,我們假定保險(xiǎn)公司收取的保費(fèi)和收取保費(fèi)的時(shí)間間隔是相依的,這種相依結(jié)構(gòu)是通過(guò)FGM-copula函數(shù)建立的,索賠過(guò)程仍是復(fù)合泊松過(guò)程.本文主要考慮兩類風(fēng)險(xiǎn)模型,第一類是在保費(fèi)隨機(jī)化模型基礎(chǔ)上直接拓展而來(lái)的風(fēng)險(xiǎn)模型,第二類是對(duì)第一類模型的進(jìn)一步推廣,即帶擾動(dòng)的風(fēng)險(xiǎn)模型,對(duì)這兩類模型的研究在保險(xiǎn)實(shí)務(wù)中有著非常重要的意義. 本文共分為三部分. 第一部分主要介紹了文章所研究的兩類風(fēng)險(xiǎn)模型以及有關(guān)的背景知識(shí).第一類模型是：第二類模型是： 第二部分討論了第一類風(fēng)險(xiǎn)模型的兩類分紅策略：障礙分紅策略和閾值分紅策略.在障礙分紅策略下,得到期望折扣罰金函數(shù)mb,δ(u；b))滿足的積分方程為：(λ1+λ2+δ)mb,δ(u;b)=λ2∫0u mb,δ(u-y;b)dF(y)+λ2∫u∞w(w,y-u)dF(y)+∫(b-u)0mb,δ(u+x;b)gx,w(x,0)dx+∫∞(b-u) mb,∧(b;b)gx,w(x,0)dx,分紅函數(shù)V(u：b)所滿足的積分方程為：(λ1+λ2+δ)V(u;b)=λ2∫u0V(u-y;b)dF(y)+∫(b-u)0V(u+x;b)gx,w(x,0)dx+∫∞b-u(u+x-b+V(b;b))gx,w(x,0)dx.在索賠額和保費(fèi)收取額都服從指數(shù)分布這種特殊情形下,我們又對(duì)其進(jìn)行了相關(guān)探討,相繼得到了破產(chǎn)時(shí)的Laplace變換和分紅函數(shù)所滿足的方程以及它們的具體表達(dá)式.在此基礎(chǔ)上,我們可以求出保費(fèi)收取額與保費(fèi)收取時(shí)間間隔相互獨(dú)立情形下的些相關(guān)量的具體表達(dá)式,得到的結(jié)果與之前的結(jié)論相吻合.在閾值分紅策略下,分紅函數(shù)滿足的積分微分方程為：當(dāng)0ub時(shí),(λ1+λ2+δ)V1(u;b)=λ2∫u0V1(u-y;b)dF(y)+∫b-u0V1(u+x;b)gx,w(x,0)dx+∫∞b-n V2(u+x;b)gx,w(x,0)dx,當(dāng)ub時(shí),(λ1+λ2+δ)V2(u;b)=α-αV'2(u;b)+λ2∫u-00V2(u-y;b)dF(y) λ2∫αu-b V1(u-y;b)dF(y)+∫∞0V2(u+x;b)gx,w(x,0)dx.然后就索賠額和保費(fèi)收取額都服從指數(shù)分布的特殊情形,本部分以推論的形式給出了結(jié)果. 第三部分主要討論第二類風(fēng)險(xiǎn)模型.類似地,我們求出它在障礙分紅策略下的分紅函數(shù)滿足的積分微分方程為：(λ1+λ2+δ)Vσ(u;b)=1/2σ2V"σ(u;b)+λ2∫u0Vσ(u-y;b)dF(y)+∫b-u0Vσ(u+x;b)gx,w(x,0)dx+∫∞b-u(u+x-b+Vσ(b;b))gx,w(x,0)dx.在閾值分紅策略下的分紅函數(shù)所滿足的積分-微分方程為：當(dāng)0ub時(shí),(λ1+λ2+δ)V1,σ(u;b)=(σ2)/2V"1,σ(u;b)+λ2∫u0V1,σ(u-y;b)dF(y)+∫b-u0V1,σ(u+x;b)gx,w(x,0)dx∫∞b-uV2,σ(u+x;b)當(dāng)ub時(shí),(λ1+λ2+δ)V2,σ(u;b)=α-βV'2,σ(u;b)+(σ2)/2V"2,σ(u;b)+λ1∫u-b0V2,σ(u-y;b)dF(y)+λ2∫u u-b V1,σ(u-y;b)dF(y)+∫∞0V2,σ(u+x;b)gx,w(x,0)dx.除此之外,對(duì)于類似于第二部分的特殊情形,本文也進(jìn)行了詳細(xì)的討論. 本文主要討論了所研究模型在特殊情形下的分紅函數(shù)的具體表達(dá)形式,而對(duì)于更一般的情形,還尚待解決.
[Abstract]:In the field of the stochastic process and its application, the article on the insurance risk model is numerous, and people are no longer satisfied with the study of the classical risk model. So far, the model of risk model, risk model with disturbance, model of claim process, model of premium randomization, dual model and so on have been widely studied. This paper discusses a new dependent model, that is, on the basis of the model of premium randomization, we assume that the insurance premium and the time interval of the premium are dependent on the premium collection process, which is established by the FGM-coula function. The process of claim is still a compound Poisson process. In this paper, two types of risk models are considered, the first is the risk model developed directly on the basis of the model of premium randomization, and the second is the further extension of the first model, i. e. the risk model with disturbance, The study of these two models is of great importance in the practice of insurance. This paper is divided into three parts: The first part mainly introduces two types of risk models and the related back of the article. View knowledge. The first model is: the second category The model is that the second part discusses two types of bonus strategies of the first type of risk model: the strategy and the threshold of the bonus. The value bonus strategy is as follows: (1 + (2 + 1) mb, (u; b) = {2} {0 u mb,} (u; b) = {2} {0 u mb,} (u-y; b) dF (y) + {2} u (w, y-u) dF (y) + {2} u (w, y-u) dF (y) + 2 (b-u) 0mb, under an obstacle bonus strategy. (u + x; b) gx, w (x,0) dx + __ (b-u) mb, w (b; b) gx, w (x,0) dx, the integral equation satisfied by the bonus function V (u: b) is: (u; b) = {2} u0V (u-y; b) dF (y) + 2 (b-u)0 V (u + x; b) gx, w (x,0) dx + {\ b-u (u + x-}) b+V(b;b))gx,w(x (0) dx. In this special case, the amount of the claim and the amount of the premium are subject to the exponential distribution. In this special case, we have also discussed it, and the equations of the Laplace transform and the bonus function at the time of the bankruptcy have been obtained. On this basis, we can find the specific expression of some correlation between the premium collection amount and the premium collection time interval, and the result is the same as that of the previous The integral differential equation that is satisfied by the bonus function under the threshold bonus strategy is: (1 + 2 + 1) V1 (u; b) = {2} u0V1 (u-y; b) dF (y) + b-u0V1 (u + x; b) dF (y) + b-u0V1 (u + x; b) gx, w (x,0) dx + {\ b-n V2 (u + x; b) gx, w (x,0) dx , when the hub is, (+ 1 + {2 +}) V2 (u; b) = 1-2 V '2 (u; b) + {2} u-00 V2 (u-y; b) dF (y) = 2} {u-b V1 (u-y; b) dF (y) + {= 0 V2 (u + x; b) gx, w (x ,0) dx. The amount of the claim and the amount of the premium are then subject to a special case of an exponential distribution, in the form of an inference. The results are given. The third part mainly discusses The second type of risk model. Similarly, we find the integral differential equation for which the bonus function under the obstacle bonus strategy is: (1 + 2 + 2 + 1) V (u; b) = 1/2,2 V "(u; b) + {2} u0V (u-y; b) dF (y) + {b-u0V} (u + x; b) gx, w (x,0) dx + {\ b-u (u + x-b + V} (b; b)) gx, w (x,0) dx. The integral-differential equation satisfied by the bonus function under the threshold bonus strategy is: when 0 ub, (1 + 2 + 1) V1,1 (u; b) = (Sup2)/2 V" 1,1 (u; b) + {2} u0V1,1 (u-y; b) dF (y) + {b-u0V1,} (u + x; b) ) gx, w (x,0) dx {\ b-uV2,} (u + x; b) when b, (u; b) = 1-{2 +} V2,} (u; b) = 1-{V '2,} (u; b) + ({2)/2 V "2,} (u; b) + {1} u-b0V2,} (u-y; b) dF (y) + {2} u-b V 1, u (u-y; b) dF (y) + {= 0 V2,} (u + x; b) gx, w (x,0) dx. In addition, this article also The detailed discussion is given. This paper mainly discusses the specific expression of the bonus function of the model under special circumstances, and for more general
【學(xué)位授予單位】：曲阜師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：O211.67;F840.4

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 姚定俊;汪榮明;徐林;;隨機(jī)保費(fèi)風(fēng)險(xiǎn)模型下的平均折現(xiàn)罰金函數(shù)(英文)[J];應(yīng)用概率統(tǒng)計(jì);2008年03期

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