【摘要】：目前,大部分研究只考慮了保險(xiǎn)公司的投資問(wèn)題而忽略了再保險(xiǎn)公司的管理.但是再保險(xiǎn)公司也會(huì)面臨破產(chǎn),也需要投資它的資產(chǎn)到金融市場(chǎng)去管理它的財(cái)富.所以,本文主要研究了在保險(xiǎn)公司能夠購(gòu)買(mǎi)比例再保險(xiǎn)的條件下,保險(xiǎn)公司和再保險(xiǎn)公司的最優(yōu)投資問(wèn)題.并且我們得到了關(guān)于保險(xiǎn)公司的終端財(cái)富期望指數(shù)效用最大化和再保險(xiǎn)公司的終端財(cái)富期望指數(shù)效用最大化以及破產(chǎn)概率最小化的相關(guān)結(jié)論.本文主要工作如下：第一章,簡(jiǎn)單概括了保險(xiǎn)公司和再保險(xiǎn)公司的研究背景及其最新研究動(dòng)態(tài).接著介紹了本文的主要內(nèi)容及其結(jié)論.第二章,主要介紹了幾種索賠過(guò)程和盈余過(guò)程以及本文將要用到的風(fēng)險(xiǎn)市場(chǎng)投資的價(jià)格過(guò)程.第三章,首先,運(yùn)用布朗運(yùn)動(dòng)與漂移項(xiàng)刻畫(huà)了保險(xiǎn)公司的索賠過(guò)程；其次,我們認(rèn)為保險(xiǎn)公司可以購(gòu)買(mǎi)比例再保險(xiǎn)來(lái)降低潛在的風(fēng)險(xiǎn),因此得到了它的盈余過(guò)程；然后,假定保險(xiǎn)公司能夠?qū)⑺挠嘁詿o(wú)風(fēng)險(xiǎn)資產(chǎn)和風(fēng)險(xiǎn)資產(chǎn)的形式投資到金融市場(chǎng),從而得到了其財(cái)富過(guò)程,其中保險(xiǎn)公司的風(fēng)險(xiǎn)資產(chǎn)是由一個(gè)幾何布朗運(yùn)動(dòng)來(lái)刻畫(huà)的；最后,通過(guò)運(yùn)用隨機(jī)控制理論解決值函數(shù)所滿足的HJB方程,得到了保險(xiǎn)公司的最優(yōu)比例再保險(xiǎn)和終端財(cái)富期望指數(shù)效用最大化下的最優(yōu)投資策略.第四章,在第三章保險(xiǎn)公司得到的最優(yōu)比例再保險(xiǎn)的條件下,我們分別得到了再保險(xiǎn)公司在終端財(cái)富期望指數(shù)效用最大化和破產(chǎn)概率最小化條件下的最優(yōu)投資策略.然后說(shuō)明了再保險(xiǎn)公司在期望指數(shù)效用最大化和破產(chǎn)概率最小化這兩種情況下最優(yōu)投資策略的等價(jià)性.第五章,介紹了再保險(xiǎn)公司可以將它的盈余以無(wú)風(fēng)險(xiǎn)資產(chǎn)和風(fēng)險(xiǎn)資產(chǎn)的形式投資于金融市場(chǎng),其中風(fēng)險(xiǎn)資產(chǎn)是由經(jīng)典的CEV模型來(lái)刻畫(huà)的.通過(guò)解決相應(yīng)的HJB方程以及效用函數(shù)中所使用的冪變換,得到了最優(yōu)投資策略.
[Abstract]:At present, most studies only consider the investment of insurance companies and ignore the management of reinsurance companies. But the reinsurer also faces bankruptcy and needs to invest its assets in financial markets to manage its wealth. Therefore, this paper mainly studies the optimal investment of insurance companies and reinsurance companies under the condition that insurance companies can buy proportional reinsurance. Furthermore, we obtain some conclusions about the utility maximization of the end-wealth expectation index of the insurance company, the maximum utility of the end-wealth expectation index of the reinsurance company and the minimization of the ruin probability. The main work of this paper is as follows: the first chapter briefly summarizes the research background and the latest research trends of insurance companies and reinsurance companies. Then the main contents and conclusions of this paper are introduced. The second chapter mainly introduces several kinds of claim process and earnings process as well as the price process of risk market investment which will be used in this paper. In chapter 3, firstly, we use Brownian motion and drift term to describe the claim process of insurance company; secondly, we think that insurance company can buy proportional reinsurance to reduce the potential risk, so we get its surplus process. Assuming that the insurance company can invest its surplus in the financial market in the form of risk-free assets and riskless assets, the process of its wealth is obtained, in which the risky assets of the insurance company are characterized by a geometric Brownian motion; finally, By using stochastic control theory to solve the HJB equation satisfied by the value function, the optimal investment strategy of insurance companies under optimal proportional reinsurance and terminal wealth expectation index utility maximization is obtained. In chapter 4, under the condition of optimal proportional reinsurance obtained by insurance companies in chapter 3, we obtain the optimal investment strategies of reinsurance companies under the conditions of maximum utility of terminal wealth expectation index and minimization of ruin probability respectively. Then we prove the equivalence of optimal investment strategies for reinsurance companies in the case of optimal exponential utility maximization and ruin probability minimization. Chapter five introduces that the reinsurance company can invest its surplus in the financial market in the form of risk-free assets and riskless assets, in which the risky assets are described by the classical CEV model. The optimal investment strategy is obtained by solving the corresponding HJB equation and the power transformation used in the utility function.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：F224;F842.3

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