本文選題：最優(yōu)再保險 + VaR準則　； 參考：《山東師范大學》2017年碩士論文

【摘要】：再保險是保險人為了分散風險,將其所承擔的風險的一部分轉(zhuǎn)移給再保險人的一種保險.特別是當保險人面臨巨大風險時,通過再保險轉(zhuǎn)移風險是非常有必要的.而再保險中最關(guān)鍵的問題是最優(yōu)再保險,如何選擇最優(yōu)再保險形式就成為保險人迫切需要解決的問題.目前,已有大量的文獻從保險人的角度或者從再保險人的角度研究最優(yōu)再保險.而一份再保險合同涉及保險人和再保險人雙方,并且他們兩者之間具有沖突的利益關(guān)系.保險人認為最優(yōu)的再保險合同,對于再保險人來說未必是最優(yōu)的,甚至有時是難以接受的.因此,在這篇文章中,我們同時考慮保險人和再保險人雙方的利益,在VaR準則下研究帕累托最優(yōu)再保險策略,它可以由保險人和再保險人的VaR的凸組合的最小值決定.我們假設再保險保費原則滿足風險附加和保止損序的性質(zhì),根據(jù)不同的分出損失函數(shù),可以得到不同的最優(yōu)再保險策略.當分出損失函數(shù)是單調(diào)不減的凸函數(shù)時,采用幾何的方法來確定最優(yōu)再保險的策略.為了進一步證明我們已得到的結(jié)果的適用性,在再保費原則為Dutch保費原則和Wang's保費原則下,分別給出了最優(yōu)再保險策略下的最優(yōu)參數(shù).當分出損失函數(shù)是單調(diào)不減的凹函數(shù)時,求得期望值保費原則下的最優(yōu)再保險策略和最優(yōu)參數(shù).
[Abstract]:Reinsurance is a kind of insurance that the insurer transfers part of the risk to the reinsurer in order to disperse the risk. Especially when the insurer is facing huge risk, it is necessary to transfer the risk through reinsurance. The most important problem in reinsurance is optimal reinsurance. How to choose the optimal reinsurance form is an urgent problem to be solved by the insurer. At present, a large number of literatures have studied optimal reinsurance from the perspective of insurers or reinsurers. A reinsurance contract involves both the insurer and the reinsurer, and they have conflicting interests. The insurer thinks that the optimal reinsurance contract is not necessarily optimal or sometimes unacceptable to the reinsurer. Therefore, in this paper, we consider the interests of both the insurer and the reinsurer at the same time, and study Pareto optimal reinsurance strategy under the VaR criterion, which can be determined by the minimum value of the convex combination of the VaR of the insurer and the reinsurer. We assume that the reinsurance premium principle satisfies the properties of risk addition and stop loss order, and according to different loss function, we can obtain different optimal reinsurance strategies. When the loss function is a monotone convex function, the geometric method is used to determine the optimal reinsurance strategy. In order to prove the applicability of the obtained results, the optimal parameters under the optimal reinsurance policy are given under the Dutch premium principle and the Wang's premium principle, respectively. When the loss function is a monotone concave function, the optimal reinsurance strategy and the optimal parameters are obtained under the expected premium principle.
【學位授予單位】：山東師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F224;F840.69
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本文編號：1876184