本文選題：融資 + 再保險��； 參考：《海南師范大學(xué)》2017年碩士論文

【摘要】：保險公司都致力于尋找相應(yīng)的方法來減少公司所承擔(dān)的風(fēng)險.其中再保險就是是保險公司減少風(fēng)險的一種行之有效的辦法.但是如果保險公司為了降低風(fēng)險而簽訂了再保險協(xié)議,那么該公司的收益也會隨之降低.近幾年,考慮如何通過再保險策略和分紅策略來權(quán)衡公司的風(fēng)險和收益成為一個熱點問題.本文運用了隨機(jī)控制理論、最優(yōu)策略理論和HJB方程等數(shù)學(xué)理論來研究保險公司的最優(yōu)再保險、分紅和融資的決策.文章中分別考慮了一般的擴(kuò)散過程和帶有負(fù)債型擴(kuò)散過程的比例再保險、有界分紅和融資的最優(yōu)策略.我們的目標(biāo)是找到使得破產(chǎn)時期望分紅與期望融資的差達(dá)到最大的策略,并給出相應(yīng)策略的顯示表達(dá)式.在一般的擴(kuò)散模型的基礎(chǔ)上,模型的風(fēng)險和收益的增加或減少可以通過控制比例再保險、有界分紅和強(qiáng)制融資策略來達(dá)到,當(dāng)資產(chǎn)到達(dá)某個給定值的時候進(jìn)行分紅,使得破產(chǎn)時期望分紅與期望融資的差值最大,即找到最優(yōu)的值函數(shù)(期望折現(xiàn)分紅減去期望折現(xiàn)融資的最大值).通過求解模型相應(yīng)的HJB方程,我們得到了最優(yōu)值函數(shù)和最優(yōu)策略的顯示表達(dá)式.在帶有負(fù)債型擴(kuò)散模型的基礎(chǔ)上,考慮了通過控制比例再保險、有界分紅和融資權(quán)衡模型的風(fēng)險和收益,當(dāng)資產(chǎn)到達(dá)某個給定值的時候進(jìn)行分紅,使得破產(chǎn)時的期望分紅減去期望融資最大,即找到最優(yōu)的值函數(shù)(期望折現(xiàn)分紅減去期望折現(xiàn)融資的最大值).考慮了兩個不同的最優(yōu)控制問題,第一個是在不融資情況下,找到相應(yīng)的值函數(shù)和最優(yōu)策略,第二個是在融資的條件下,找到相應(yīng)的值函數(shù)和最優(yōu)策略.最后分析兩種情況,得到了一般情況下的隨機(jī)控制問題的解,給出了什么條件下選擇融資,什么條件下選擇不融資最有利.
[Abstract]:Insurance companies are working to find ways to reduce the risks they take. Reinsurance is an effective way for insurance companies to reduce risk. But if the insurer signs a reinsurance agreement to reduce risk, the company's earnings will also fall. In recent years, it has become a hot issue to consider how to weigh the risk and income of the company through reinsurance strategy and dividend strategy. In this paper, stochastic control theory, optimal strategy theory and HJB equation are used to study the optimal reinsurance, dividend and financing decisions of insurance companies. In this paper, the optimal strategies of general diffusion process and proportional reinsurance with debt diffusion process, bounded dividend and financing are considered respectively. Our goal is to find the strategy to maximize the difference between the expected dividend and the expected financing at the time of bankruptcy, and give the corresponding expression of the strategy. On the basis of the general diffusion model, the increase or decrease of the risk and income of the model can be achieved by controlling proportional reinsurance, bounded dividend and compulsory financing strategy, when the asset reaches a given value. The difference between the expected dividend and the expected financing is the largest in bankruptcy, that is, the optimal value function is found (the expected discount dividend minus the maximum value of the expected discount financing). By solving the corresponding HJB equation of the model, we obtain the display expressions of the optimal value function and the optimal strategy. Based on the debt-type diffusion model, the risks and benefits of the model are considered by controlling proportional reinsurance, bounded dividends and financing, and dividends are paid when the assets reach a given value. When the expected dividend is reduced by the maximum expected financing, the optimal value function is found (the expected discount dividend minus the maximum value of the expected discount financing). Two different optimal control problems are considered. The first is to find the corresponding value function and optimal strategy without financing, and the second is to find the corresponding value function and optimal strategy under the condition of financing. Finally, by analyzing the two kinds of cases, we obtain the solution of the stochastic control problem under general circumstances, and give out the conditions under which financing is chosen and under what conditions it is most advantageous to choose no financing.
【學(xué)位授予單位】：海南師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F840.31;O211.67

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 林祥;楊鵬;;擴(kuò)散風(fēng)險模型下再保險和投資對紅利的影響[J];經(jīng)濟(jì)數(shù)學(xué);2010年01期

相關(guān)碩士學(xué)位論文 前1條

1 王丹;保險公司最優(yōu)投資和再保險策略[D];燕山大學(xué);2014年

，

本文編號：1798861