本文選題：風(fēng)險(xiǎn)模型 + 破產(chǎn)概率�。� 參考：《寧夏大學(xué)》2014年碩士論文

【摘要】：保險(xiǎn)公司在金融機(jī)構(gòu)中發(fā)揮著越來越重要的作用,但競(jìng)爭(zhēng)也日趨激烈,僅僅依靠保險(xiǎn)索賠賺取收入的增長(zhǎng)方式已經(jīng)不可持續(xù).與此同時(shí),保險(xiǎn)公司擁有大量的現(xiàn)金流,公司管理層如何能有效地運(yùn)營資本和規(guī)避風(fēng)險(xiǎn)尤顯重要. 本文建立了三個(gè)更加符合市場(chǎng)現(xiàn)狀和具有經(jīng)濟(jì)意義的模型,通過借助概率與隨機(jī)分析的思想,構(gòu)造HJB方程,得到了最優(yōu)回報(bào)函數(shù)和相應(yīng)的最優(yōu)控制策略.主要工作包括： 1.考慮了變破產(chǎn)下限的單險(xiǎn)種風(fēng)險(xiǎn)模型,其破產(chǎn)概率不易求得,但給出了破產(chǎn)概率上界的不等式,此不等式為風(fēng)險(xiǎn)管理提供了有力的工具,對(duì)保險(xiǎn)公司管理層如何選擇其經(jīng)營策略有一定的指導(dǎo)意義. 2.考慮了保險(xiǎn)公司通過連續(xù)購買比例再保險(xiǎn)控制和管理風(fēng)險(xiǎn)的同時(shí)又將公司固定比例的盈余資本投資到風(fēng)險(xiǎn)市場(chǎng)的情況.事實(shí)上,在我國,并不允許保險(xiǎn)公司將所有盈余資本投資到風(fēng)險(xiǎn)市場(chǎng).因此,將公司總盈余的固定比例投資于風(fēng)險(xiǎn)市場(chǎng)更具有現(xiàn)實(shí)意義. 3.假定資本市場(chǎng)變動(dòng)與保險(xiǎn)公司資本收益變動(dòng)存在相關(guān)性的情況下,利用HJB-變分不等方程求解出最優(yōu)再保險(xiǎn)策略和最小破產(chǎn)概率的顯示表達(dá)式.最后討論了受這種相關(guān)性影響的一些定量分析.
[Abstract]:Insurance companies play a more and more important role in financial institutions, but the competition is becoming more and more fierce. At the same time, insurance companies have a lot of cash flow, how the management can effectively operate capital and avoid risk is particularly important. In this paper, three models which are more in line with the market situation and have economic significance are established. By using the idea of probability and stochastic analysis, the HJB equation is constructed, and the optimal return function and corresponding optimal control strategy are obtained. The main tasks include: 1. The ruin probability of a single insurance risk model with variable ruin limit is considered. However, the inequality of upper bound of ruin probability is given, which provides a powerful tool for risk management. It has certain guiding significance to how to choose the management strategy of insurance company. 2. This paper considers the situation that the insurance company controls and manages the risk through the continuous purchase proportion reinsurance, and at the same time it invests the company's fixed proportion of surplus capital in the risk market. In fact, insurance companies are not allowed to invest all surplus capital in the risk market in China. Therefore, it is more practical to invest the fixed proportion of total earnings in the risk market. 3. Assuming the correlation between capital market change and capital income change of insurance companies, the optimal reinsurance strategy and the display expression of minimum ruin probability are obtained by using HJB- variational inequality equation. Finally, some quantitative analyses affected by this correlation are discussed.
【學(xué)位授予單位】：寧夏大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F840;O232

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