本文選題：稀疏過程　切入點(diǎn)：保費(fèi)隨機(jī)化　出處：《曲阜師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：經(jīng)典風(fēng)險(xiǎn)模型中以常數(shù)比率收取保費(fèi),但在保險(xiǎn)公司的現(xiàn)實(shí)經(jīng)營中,保費(fèi)的收入是隨機(jī)的,且通常是與索賠的發(fā)生相關(guān)的.因此,本文中考慮了一類相依結(jié)構(gòu)的稀疏風(fēng)險(xiǎn)模型,在該模型中,假設(shè)保單的到達(dá)過程是參數(shù)為λ的Poisson過程,同時(shí)索賠到達(dá)過程是該P(yáng)oisson過程的一個(gè)P-稀疏過程.Gerber與Shiu(1998)首先提出了Gerber-Shiu函數(shù)(也稱為期望折現(xiàn)罰金函數(shù)),提供了一個(gè)可以同時(shí)解決多個(gè)精算量的統(tǒng)一方法.De Finetti(1957)初次提出了分紅問題,目前分紅問題是研究熱點(diǎn).本文考慮了一類稀疏風(fēng)險(xiǎn)模型,研究了在常數(shù)barrier策略和周期分紅策略下的期望折現(xiàn)罰金函數(shù)和期望折現(xiàn)累計(jì)分紅函數(shù),得到了它們分別所滿足的積分方程,同時(shí)也獲得了在特殊情況下的具體表達(dá)式以及破產(chǎn)概率的精確表達(dá)式.第一章為緒論,介紹了一類相依結(jié)構(gòu)的稀疏風(fēng)險(xiǎn)模型,以及周期分紅研究的背景及現(xiàn)狀.第二章為預(yù)備知識(shí)和模型介紹,重點(diǎn)介紹了稀疏風(fēng)險(xiǎn)模型和周期分紅策略,以及Gerber-Shiu函數(shù)等基本概念.第三章和第四章是本文中的主要研究成果,第三章得到了帶有周期分紅策略的稀疏風(fēng)險(xiǎn)模型的期望折現(xiàn)罰金函數(shù)所滿足的積分方程當(dāng),當(dāng)u b時(shí).同時(shí)得到了在索賠額和保費(fèi)額同時(shí)服從指數(shù)分布時(shí)的期望折現(xiàn)罰金函數(shù)的具體表示式最后獲得了破產(chǎn)概率的精確表達(dá)式第四章主要研究了帶有周期分紅策略的稀疏風(fēng)險(xiǎn)模型的期望折現(xiàn)累計(jì)分紅函數(shù)所滿足的積分方程當(dāng)0 ≤ u ≤ 6 時(shí),當(dāng)u 6時(shí),.以及在索賠額和保費(fèi)額同時(shí)服從指數(shù)分布時(shí)的期望折現(xiàn)累計(jì)分紅函數(shù)的精確表達(dá)式.第五章對(duì)本文進(jìn)行了總結(jié).
[Abstract]:In the classical risk model, the premium is charged at a constant rate, but in the real operation of an insurance company, the premium income is random and usually related to the occurrence of claims. Therefore, a class of sparse risk models with dependent structures are considered in this paper. In this model, it is assumed that the policy arrival process is a Poisson process with a parameter 位. The simultaneous claim arrival process is a P- sparse process of the Poisson process. Gerber and Shiu (1998) first proposed the Gerber-Shiu function (also known as the expected discounted penalty function, which provides a unified method to solve multiple actuarial quantities simultaneously. De Finettitio 1957). The issue of dividends is raised. In this paper, we consider a kind of sparse risk model, and study the expected discounted penalty function and the expected discounted cumulative dividend function under the constant barrier strategy and the periodic dividend policy. The integral equations which they satisfy are obtained respectively. At the same time, the concrete expressions and the exact expressions of ruin probability in special cases are obtained. The first chapter is an introduction, which introduces a class of sparse risk models with dependent structures. The second chapter is the introduction of preparatory knowledge and model, focusing on sparse risk model and periodic dividend strategy. Chapter 3 and chapter 4th are the main research results in this paper. In chapter 3, the integral equation of the expected discounted penalty function of the sparse risk model with periodic dividend strategy is obtained. When u b, the exact expression of the expected discounted penalty function for both the claim amount and the premium amount is obtained. Finally, the exact expression of ruin probability is obtained in Chapter 4th. The integral equation satisfied by the expected discounted cumulative dividend function of sparse risk model of red strategy is 0 鈮，

本文編號(hào)：1640215