發(fā)布時(shí)間：2018-01-31 06:42

  本文關(guān)鍵詞： 超額損失再保險(xiǎn) HJB方程 投資 破產(chǎn)概率 擴(kuò)散逼近　出處：《蘭州理工大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：最優(yōu)投資與再保險(xiǎn)是近年來(lái)金融學(xué)研究的熱點(diǎn)問(wèn)題之一,由于保險(xiǎn)行業(yè)競(jìng)爭(zhēng)激烈,為了增強(qiáng)企業(yè)競(jìng)爭(zhēng)力,一方面,保險(xiǎn)公司需要在金融市場(chǎng)上進(jìn)行投資來(lái)獲得收益,以提高公司的償付能力和公司效益,而投資是保險(xiǎn)公司獲得資金的主要渠道之一；另一方面,為了減少大賠付的風(fēng)險(xiǎn),保險(xiǎn)公司需要分出部分保費(fèi)來(lái)購(gòu)買再保險(xiǎn),再保險(xiǎn)可以使風(fēng)險(xiǎn)在各保險(xiǎn)公司之間進(jìn)行進(jìn)行分?jǐn)?不僅可以提高保險(xiǎn)經(jīng)營(yíng)的效率,同時(shí),也促進(jìn)了保險(xiǎn)業(yè)經(jīng)營(yíng)的穩(wěn)定性,實(shí)現(xiàn)了保險(xiǎn)企業(yè)之間的利益共享和風(fēng)險(xiǎn)共擔(dān).因此,研究最優(yōu)投資與再保險(xiǎn)的策略問(wèn)題,對(duì)保險(xiǎn)公司具有很重要的理論基礎(chǔ)和現(xiàn)實(shí)意義. 本文是利用隨機(jī)控制理論的方法,通過(guò)建立數(shù)學(xué)模型研究了最優(yōu)再保險(xiǎn)與投資策略,以及如何提高自身的盈余水平和賠付能力使得保險(xiǎn)公司破產(chǎn)概率最小的最優(yōu)控制問(wèn)題.首先,在帶漂移系數(shù)的風(fēng)險(xiǎn)模型下,保險(xiǎn)公司購(gòu)買超額損失再保險(xiǎn),并將部分盈余投資于一些風(fēng)險(xiǎn)資產(chǎn)和無(wú)風(fēng)險(xiǎn)資產(chǎn)；其次,用擴(kuò)散逼近的原理使離散的賠付過(guò)程連續(xù)化,得出了相應(yīng)HJB方程的顯式解,并證明了相關(guān)解的存在性與唯一性,并總結(jié)出在不同自留額下的最小破產(chǎn)概率、最優(yōu)超額損失再保險(xiǎn)和最優(yōu)投資策略；最后,用MATLAB軟件通過(guò)數(shù)值模擬計(jì)算分析了一些重要參數(shù)對(duì)最優(yōu)超額損失再保險(xiǎn)策略、最優(yōu)投資策略和最小破產(chǎn)概率的影響,驗(yàn)證和得出了一些重要的結(jié)論.
[Abstract]:Optimal investment and reinsurance is one of the hot issues in finance research in recent years. Because of the fierce competition in the insurance industry, in order to enhance the competitiveness of enterprises, on the one hand. Insurance companies need to invest in the financial market to obtain income in order to improve the solvency and efficiency of the company, and investment is one of the main channels for insurance companies to obtain funds. On the other hand, in order to reduce the risk of large claims, insurance companies need to allocate part of the premium to buy reinsurance, reinsurance can make the risk between the insurance companies to share. It can not only improve the efficiency of insurance management, but also promote the stability of insurance business, realize the benefit sharing and risk sharing among insurance companies. It has important theoretical basis and practical significance for insurance companies. In this paper, the optimal reinsurance and investment strategy are studied by means of stochastic control theory and mathematical model. And how to improve their earnings level and the ability to pay the insurance companies to make the minimum probability of bankruptcy optimal control problem. Firstly, under the risk model with drift coefficient, insurance companies buy excess loss reinsurance. Part of the surplus is invested in some risky assets and risk-free assets; Secondly, the discrete compensation process is continuous by the principle of diffusion approximation, the explicit solution of the corresponding HJB equation is obtained, and the existence and uniqueness of the correlation solution are proved. The minimum ruin probability, the optimal excess loss reinsurance and the optimal investment strategy are summarized. Finally, the effects of some important parameters on the optimal excess loss reinsurance strategy, optimal investment strategy and minimum ruin probability are analyzed by numerical simulation with MATLAB software. Some important conclusions are obtained.
【學(xué)位授予單位】：蘭州理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F840;F224

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