【摘要】：再保險是保險公司的一個有效風(fēng)險管理工具,保險公司通過平衡分出損失和再保險保費,將部分風(fēng)險轉(zhuǎn)移到再保險公司來控制其風(fēng)險.衡量最優(yōu)再保險的常見標(biāo)準(zhǔn)可以分為以下三類:方差最小化、效用函數(shù)最大化以及破產(chǎn)概率最小.近幾年,許多學(xué)者應(yīng)用風(fēng)險度量來研究最優(yōu)再保險.因此,我們通過風(fēng)險度量來研究最優(yōu)性再保險策略.主要內(nèi)容概述如下:第一章,介紹了再保險的研究背景、研究現(xiàn)狀以及本文的研究內(nèi)容.第二章,介紹了再保險的定義、常見的保費原理及風(fēng)險度量.第三章,我們以停止-損失再保險作為研究對象.在和風(fēng)險度量下,提出了一個變量變換方法分別得到了和風(fēng)險度量下停止損失再保險的最優(yōu)自留額.假設(shè)是保險人的初始損失,對應(yīng)的累計分布函數(shù)為(3()=((3≤)并且生存函數(shù)為.記變換為,首先,分析了變量和的性質(zhì).然后,在VaR和CTE最優(yōu)化標(biāo)準(zhǔn)下,我們給出了對應(yīng)自留額存在的充分必要條件.最后,得到對應(yīng)的最優(yōu)自留額.給出一些例子對以上的結(jié)果進(jìn)行說明.第四章,考慮了再保險人違約風(fēng)險的影響,研究了在風(fēng)險度量下的最優(yōu)再保險.在再保險合同中,再保險人承諾支付保險人面臨的部分損失通過向保險人收取一定的保費.然而,當(dāng)再保險人承諾支付的限額超過了他自己的償付能力,則違約風(fēng)險發(fā)生.因此考慮了違約風(fēng)險并且對再保險人的初始資本進(jìn)行一定的限定是必要的.在(2(69)2)′保費原理下,應(yīng)用風(fēng)險度量VaR的最優(yōu)化標(biāo)準(zhǔn)使得保險人的總風(fēng)險最小得到分層再保險是最優(yōu)的.最后,給出相應(yīng)的數(shù)值算例.第五章,應(yīng)用扭曲風(fēng)險度量和扭曲保費原理建立了含有違約風(fēng)險的總風(fēng)險模型.首先,通過邊際索賠(MIF)函數(shù)與分出函數(shù)之間的關(guān)系建立了與總風(fēng)險模型等價的MIF再保險優(yōu)化模型.然后對MIF再保險優(yōu)化模型的求解得到最優(yōu)的邊際索賠(MIF)函數(shù),進(jìn)而得到最優(yōu)的分出函數(shù).最后,應(yīng)用該方法研究了在VaR風(fēng)險度量和Wang’s保費原理下的最優(yōu)分出函數(shù).第六章,對本文的研究結(jié)果進(jìn)行了討論和總結(jié).
[Abstract]:Reinsurance is an effective risk management tool for insurance companies. By balancing losses and reinsurance premiums, insurance companies transfer some of the risks to reinsurance companies to control their risks. The common criteria for measuring optimal reinsurance can be divided into the following three categories: minimum variance, maximization of utility function and minimum ruin probability. In recent years, many scholars use risk measurement to study optimal reinsurance. Therefore, we study the optimal reinsurance strategy through risk measurement. The main contents are summarized as follows: the first chapter introduces the research background of reinsurance, the research status and the research content of this paper. The second chapter introduces the definition of reinsurance, the common premium principle and risk measurement. In the third chapter, we take stop-loss reinsurance as the research object. Under the condition of sum risk measurement, a variable transformation method is proposed to obtain the optimal retention amount of stop loss reinsurance under and risk measurement, respectively. Suppose it is the initial loss of the insurer, the corresponding cumulative distribution function is (3 () = (3 鈮，

本文編號：2494105