發(fā)布時(shí)間：2018-02-14 04:15

  本文關(guān)鍵詞： 分紅策略 雙險(xiǎn)種 破產(chǎn)概率 Erlang(2)過(guò)程 相依索賠　出處：《廣西大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著社會(huì)經(jīng)濟(jì)的快速發(fā)展加劇了保險(xiǎn)市場(chǎng)的競(jìng)爭(zhēng),單一性質(zhì)的險(xiǎn)種已經(jīng)不能滿足社會(huì)的需求,因此建立多險(xiǎn)種的風(fēng)險(xiǎn)模型來(lái)描述保險(xiǎn)公司的經(jīng)營(yíng)情況已經(jīng)成為現(xiàn)在學(xué)者們研究的熱點(diǎn)之一.因此本文主要致力于對(duì)雙險(xiǎn)種風(fēng)險(xiǎn)模型作進(jìn)一步的推廣,建立相應(yīng)的風(fēng)險(xiǎn)模型.主要內(nèi)容為如下:1、首先研究了一類帶有隨機(jī)分紅策略下的復(fù)合二項(xiàng)雙險(xiǎn)種風(fēng)險(xiǎn)模型,其兩種索賠都是服從復(fù)合二項(xiàng)分布,當(dāng)公司盈余達(dá)到或超過(guò)紅利邊界時(shí),以概率q0支付一單位的紅利.得到了該模型期望折現(xiàn)罰金函數(shù)的遞推公式及其漸進(jìn)估計(jì)解,最后作為應(yīng)用我們還得到了破產(chǎn)概率、破產(chǎn)赤字分布函數(shù)和破產(chǎn)前盈余概率函數(shù)的遞推公式和漸近解.2、其次考慮稀疏、隨機(jī)干擾、利率等因素,建立一類雙險(xiǎn)種模型,其兩類索賠分別服從泊松分布和負(fù)二項(xiàng)分布,利用鞅論知識(shí)導(dǎo)出了該模型破產(chǎn)概率的表達(dá)式和Lundberg不等式.3、最后討論一類索賠相依的雙險(xiǎn)種模型,其索賠分別服從Poisson分布和Erlang(2)分布,推導(dǎo)出了該模型的破產(chǎn)概率、破產(chǎn)前盈余的概率函數(shù)、破產(chǎn)時(shí)刻赤字的分布函數(shù)及其聯(lián)合分布函數(shù)所滿足的積分方程,最后求出了其生存概率滿足的線性微分方程,并給出具體實(shí)例.
[Abstract]:With the rapid development of social economy, the competition of insurance market has been intensified, and the single type of insurance can no longer meet the needs of the society. Therefore, it has become one of the hot topics for scholars to establish a risk model of multiple types of insurance to describe the operation of insurance companies. Therefore, this paper is mainly devoted to the further promotion of the risk model of double insurance. A corresponding risk model is established. The main contents are as follows: 1. Firstly, a kind of compound binomial insurance risk model with random dividend strategy is studied. The two claims are subordinate binomial distribution. When the earnings of the company reach or exceed the dividend boundary, a unit dividend is paid with probability Q0. The recursive formula of the expected discounted penalty function of the model and its asymptotic estimation solution are obtained. Finally, as an application, we also obtain the ruin probability. The recursive formula and asymptotic solution of the ruin deficit distribution function and the surplus probability function before bankruptcy. Secondly, considering the factors such as sparsity, random disturbance and interest rate, a kind of double insurance model is established, in which the two kinds of claims are followed by Poisson distribution and negative binomial distribution, respectively. By using martingale theory, the expression of ruin probability and Lundberg inequality. 3 are derived. Finally, a class of double insurance models with dependent claims are discussed. The ruin probability of the model is derived from Poisson distribution and Erlang2 distribution, respectively. The probability function of surplus before ruin, the distribution function of letterhead and the integral equation satisfied by its joint distribution function are obtained. Finally, the linear differential equation of its survival probability is obtained, and a concrete example is given.
【學(xué)位授予單位】：廣西大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F840

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