本文選題：生存概率 + 互助保險(xiǎn)�。� 參考：《安徽工程大學(xué)》2017年碩士論文

【摘要】：風(fēng)險(xiǎn)是現(xiàn)代金融的一個(gè)本質(zhì)特征,其中保險(xiǎn)公司的生存概率是金融風(fēng)險(xiǎn)理論研究的重要內(nèi)容。從風(fēng)險(xiǎn)管理的角度看,保險(xiǎn)公司不能離開金融市場或其他保險(xiǎn)和再保險(xiǎn)公司而孤立的運(yùn)作。保險(xiǎn)公司和投保人為了在一定風(fēng)險(xiǎn)下獲得最大收益或?yàn)楸ＷC一定收益下風(fēng)險(xiǎn)最小必然要對風(fēng)險(xiǎn)和收益進(jìn)行選擇,相對來說,互助保險(xiǎn)具有一定的優(yōu)勢。比如船舶碰撞、石油污染、颶風(fēng)和地震等災(zāi)難性事件造成大規(guī)模的損失(索賠)的發(fā)生,不同的保險(xiǎn)公司之間通過互助保險(xiǎn),將一些風(fēng)險(xiǎn)和利潤轉(zhuǎn)移到另一家保險(xiǎn)公司,使其避免破產(chǎn)。研究風(fēng)險(xiǎn)理論的過程中提出了各種各樣的風(fēng)險(xiǎn)模型,盈余過程是風(fēng)險(xiǎn)理論研究的核心,因此在互助保險(xiǎn)的條件下研究兩個(gè)公司的盈余問題,即研究模型的破產(chǎn)概率(生存概率)等一系列問題具有一定的理論價(jià)值和現(xiàn)實(shí)意義。本文首先給出了有關(guān)風(fēng)險(xiǎn)模型的一些理論知識;然后在二元Cramer-Lundberg風(fēng)險(xiǎn)過程下,且兩個(gè)保險(xiǎn)公司之間擁有互相彌補(bǔ)虧損協(xié)議的基礎(chǔ)上,首先,考慮兩個(gè)保險(xiǎn)公司索賠到達(dá)率均服從非齊次Poisson過程時(shí),用鞅方法得到一元風(fēng)險(xiǎn)過程有限時(shí)間破產(chǎn)概率的一個(gè)上界并結(jié)合二元生存概率Laplace變換的核方程,得到二元Cramer-Lundberg風(fēng)險(xiǎn)過程下兩個(gè)保險(xiǎn)公司生存概率的一個(gè)下界,及兩個(gè)保險(xiǎn)公司險(xiǎn)種的個(gè)體索賠額均服從指數(shù)分布時(shí)生存概率的下界估計(jì);其次,考慮復(fù)合Poisson過程和復(fù)合二項(xiàng)分布兩個(gè)模型分別關(guān)于兩個(gè)保險(xiǎn)公司同時(shí)生存時(shí)索賠額之間基于Copula的相關(guān)關(guān)系,對索賠到達(dá)率服從齊次復(fù)合Poisson過程的二元Cramer-Lundberg風(fēng)險(xiǎn)模型給出兩個(gè)保險(xiǎn)公司的聯(lián)合生存概率的積分一微分方程及在二項(xiàng)分布下給出了兩個(gè)保險(xiǎn)公司的聯(lián)合生存概率的遞推公式。最后,研究了兩個(gè)保險(xiǎn)公司具有不確定性收入或支出情況下的破產(chǎn)概率,給出相應(yīng)破產(chǎn)概率所滿足的顯示表達(dá)式。最后,對本文的研究結(jié)果作出了相應(yīng)的總結(jié),給出了本文的展望。
[Abstract]:Risk is an essential feature of modern finance, in which the survival probability of insurance company is an important part of financial risk theory. From a risk management perspective, insurance companies cannot operate in isolation from financial markets or other insurance and reinsurance companies. The insurance company and the policy holder must choose the risk and the income in order to obtain the maximum benefit under certain risk or to guarantee the risk minimum under the certain income, comparatively speaking, the mutual insurance has certain superiority. Catastrophic events such as ship collisions, oil pollution, hurricanes and earthquakes caused massive losses (claims), and different insurance companies transferred some risks and profits to another insurance company through mutual insurance. To avoid bankruptcy. In the course of studying risk theory, various risk models are put forward. Earnings process is the core of risk theory research, so the earnings problem of two companies is studied under the condition of mutual insurance. In other words, the study of ruin probability (survival probability) of the model has certain theoretical value and practical significance. In this paper, we first give some theoretical knowledge about risk model, then in the process of binary Cramer-Lundberg risk, and the two insurance companies have a mutual loss compensation agreement, first, When the claim arrival rates of two insurance companies are satisfied with the inhomogeneous Poisson process, an upper bound of the finite time ruin probability of the one-variable risk process is obtained by using the martingale method and the kernel equation of the Laplace transformation of the binary survival probability is obtained. We obtain a lower bound of the survival probability of two insurance companies in the process of binary Cramer-Lundberg risk, and an estimate of the survival probability of the two insurance companies from the exponential distribution. Considering the two models of compound Poisson process and compound binomial distribution, respectively, the correlation based on Copula between the claims of two insurance companies is considered. In this paper, the integro-differential equation of the joint survival probability of two insurance companies and the recurrence formula of the joint survival probability of two insurance companies are given under the binomial distribution for the binary Cramer-Lundberg risk model of the claim arrival rate from homogeneous composite Poisson process. Finally, the ruin probability of two insurance companies with uncertain income or expenditure is studied, and the expression of the corresponding ruin probability is given. Finally, the research results of this paper are summarized, and the prospect of this paper is given.
【學(xué)位授予單位】：安徽工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O211.67

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