本文選題：破產(chǎn)概率 + 生存概率　； 參考：《河南師范大學(xué)》2017年碩士論文

【摘要】：在實(shí)際的保險業(yè)務(wù)中,保險公司不僅會開展多險種業(yè)務(wù),而且許多險種的索賠也不是只有一種,存在單一險種的多索賠的情形.本文以此為出發(fā)點(diǎn)考慮了帶有多索賠情形的風(fēng)險模型,主要研究內(nèi)容如下:(1)考慮了一類帶干擾的單險種多索賠情形的風(fēng)險模型.假設(shè)保單到達(dá)過程為Poisson過程,各情形索賠到達(dá)過程為保單到達(dá)過程的隨機(jī)p^稀疏過程,首先證明了調(diào)節(jié)系數(shù)的存在唯一性,然后利用鞅的不等式及性質(zhì),得到了該模型下破產(chǎn)概率的Lundberg不等式及一般表達(dá)式.(2)考慮了一類多險種多索賠情形的風(fēng)險模型.首先,得到了破產(chǎn)概率的Lund-berg不等式及一般表達(dá)式.然后,通過模型轉(zhuǎn)換,考慮充分小時段內(nèi)的索賠情況,利用全概率公式得到了生存概率所滿足的積分-微分方程.最后.考慮兩險種且索賠額服從指數(shù)分布這一特定情況,結(jié)合前面得到的積分-微分方程和經(jīng)典風(fēng)險理論的結(jié)果,給出了該特定情況下破產(chǎn)概率的顯式表達(dá)式.(3)考慮了一類兩險種多索賠情形的相依風(fēng)險模型.前面幾節(jié),研究了索賠過程都為Poisson過程的情形,得到了破產(chǎn)概率的Lundberg不等式及一般表達(dá)式,生存概率的積分-微分方程和索賠額服從指數(shù)分布情形下的破產(chǎn)概率顯示表達(dá)式.最后,對原風(fēng)險模型的相依部分進(jìn)行了一些轉(zhuǎn)變,得到了破產(chǎn)概率的一些結(jié)果.
[Abstract]:In the actual insurance business, the insurance company will not only carry out multi-insurance business, but also many kinds of insurance claims are not only one, there is a single type of multi-claim situation. In this paper, a risk model with multiple claims is considered. The main contents of this study are as follows: (1) the risk model of a class of single-type multiple claims with interference is considered. Assuming that the policy arrival process is a Poisson process and the claim arrival process is a stochastic p ^ sparse process of the policy arrival process, the existence and uniqueness of the adjustment coefficient are first proved, and then the martingale inequality and properties are used. The Lundberg inequality and general expression of ruin probability under this model are obtained. Firstly, the Lund-berg inequality and general expression of ruin probability are obtained. Then, through the model transformation, considering the claim in sufficient small period, the integro-differential equation of survival probability is obtained by using the full probability formula. Finally. Considering the special case of two kinds of insurance and the exponential distribution of the claimed amount, combining the results of the previous integro-differential equation and classical risk theory, In this paper, the explicit expression of ruin probability in this particular case is given. The dependent risk model for a class of multi-claim cases with two types of insurance is considered. In the previous sections, we studied the case that the claim process is a Poisson process, obtained the Lundberg inequality and the general expression of the ruin probability, the integro-differential equation of the survival probability and the expression of the ruin probability under the condition of exponential distribution of the claim amount. Finally, some changes are made to the dependent parts of the original risk model, and some results of the ruin probability are obtained.
【學(xué)位授予單位】：河南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F840.4

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 牛銀菊;鄧麗;馬崇武;;常利率下帶投資的多險種風(fēng)險模型的破產(chǎn)概率[J];江西師范大學(xué)學(xué)報(自然科學(xué)版);2015年03期

2 吳傳菊;張成林;何曉霞;熊丹;李青青;;一類相依兩險種風(fēng)險模型的分類破產(chǎn)概率（英文）[J];數(shù)學(xué)雜志;2014年05期

3 吳傳菊;張成林;王曉光;何曉霞;熊丹;;指數(shù)索賠情形下一類相依兩險種風(fēng)險模型的破產(chǎn)概率[J];數(shù)學(xué)的實(shí)踐與認(rèn)識;2014年08期

4 呂東東;趙明清;李發(fā)高;;一類推廣的復(fù)合Poisson-Geometric相依風(fēng)險模型的破產(chǎn)概率[J];經(jīng)濟(jì)數(shù)學(xué);2013年04期

5 劉文震;王傳玉;;帶擾動的兩類相關(guān)索賠風(fēng)險模型的折現(xiàn)罰金函數(shù)[J];中國科學(xué)技術(shù)大學(xué)學(xué)報;2013年06期

6 趙永霞;王春偉;;帶擾動的兩類索賠風(fēng)險模型的罰金折扣函數(shù)[J];高校應(yīng)用數(shù)學(xué)學(xué)報A輯;2010年03期

7 周麗;;相依索賠Poisson風(fēng)險模型的Cramer-Lundberg逼近(英文)[J];數(shù)學(xué)雜志;2010年03期

8 范慶祝;尹傳存;;帶紅利的兩類索賠風(fēng)險模型的Gerber-Shiu函數(shù)[J];工程數(shù)學(xué)學(xué)報;2009年01期

9 廖基定;龔日朝;劉再明;鄒捷中;;復(fù)合Poisson-Geometric風(fēng)險模型Gerber-Shiu折現(xiàn)懲罰函數(shù)[J];應(yīng)用數(shù)學(xué)學(xué)報;2007年06期

10 邢永勝;張春生;;帶干擾的Erlang(2)風(fēng)險模型的不破產(chǎn)概率[J];應(yīng)用數(shù)學(xué)學(xué)報;2006年01期

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