發(fā)布時(shí)間：2018-04-27 13:12

  本文選題：投資再保險(xiǎn)策略 + 效用函數(shù)�。� 參考：《華東師范大學(xué)》2017年博士論文

【摘要】：保險(xiǎn)公司作為市場(chǎng)經(jīng)濟(jì)中不可或缺的一環(huán),通過向個(gè)人和集體售賣保單而獲取保費(fèi)并為其提供金融保護(hù)。對(duì)于所獲得的利潤(rùn)保險(xiǎn)人可以將其投資到金融市場(chǎng)之中,通過購(gòu)買股票債券等形式獲取更大的收益。但由于資金與規(guī)模的限制,保險(xiǎn)公司有時(shí)候還需要將自己承擔(dān)的一部分保險(xiǎn)風(fēng)險(xiǎn)和收益轉(zhuǎn)讓給再保險(xiǎn)公司,即支付一定量的再保費(fèi)而換取再保險(xiǎn)公司去承擔(dān)一部分保險(xiǎn)風(fēng)險(xiǎn)損失。在這樣的經(jīng)營(yíng)過程中,一個(gè)自生的問題是如何選擇投資股票和債券的額度以及購(gòu)買再保險(xiǎn)的數(shù)量和種類。我們將這樣一類問題歸結(jié)為最優(yōu)投資再保險(xiǎn)問題。本文對(duì)不同模型下的最優(yōu)投資再保險(xiǎn)策略的相關(guān)問題展開若干研究。主要工作如下:(1)針對(duì)較廣義的兩段式效用函數(shù)模型,我們?cè)诘诙�章討論了相關(guān)的最優(yōu)投資再保險(xiǎn)策略和值函數(shù)的形式�；�于鞅理論和凸優(yōu)化的方法,我們將原本動(dòng)態(tài)的最優(yōu)化問題轉(zhuǎn)變成求解一個(gè)靜態(tài)最優(yōu)化問題的解。通過得到的終端變量的形式求解相關(guān)的條件期望,比較后獲得最優(yōu)投資再保險(xiǎn)策略的形式。此外我們還給出了所求形式下常見的幾個(gè)效用函數(shù)的最優(yōu)策略。(2)對(duì)于財(cái)險(xiǎn)型的保險(xiǎn)公司,方差保費(fèi)原理有著更加廣泛的應(yīng)用和實(shí)際意義。第三章中我們將基于方差保費(fèi)原理之下考慮保險(xiǎn)人的最優(yōu)投資再保險(xiǎn)問題。為了能夠更好的描述市場(chǎng)的變化我們用一個(gè)連續(xù)時(shí)間的馬氏鏈去描述模型參數(shù)的變化也即經(jīng)典的Regime-Switching模型,并考慮了兩種不同風(fēng)險(xiǎn)模型下的最優(yōu)策略。此外我們還對(duì)保險(xiǎn)人能夠投資到證券市場(chǎng)的金額以及所能購(gòu)買的再保險(xiǎn)份額進(jìn)行了限制,使得我們的模型更具有實(shí)際意義。(3)在以往的工作中,最優(yōu)再保險(xiǎn)問題大都是基于保險(xiǎn)人的角度去考慮的。文獻(xiàn)中很少將最優(yōu)再保險(xiǎn)問題從再保險(xiǎn)人的角度或者雙方的角度去考慮。然而作為一個(gè)由保險(xiǎn)人和再保險(xiǎn)人雙方共同制定的再保險(xiǎn)合約,僅考慮保險(xiǎn)人的角度從某種意義上來說是不完整的。換句話說,一個(gè)再保險(xiǎn)合約僅考慮任何一方的利益都可能為另一方所不接受。第四章中我們將兼顧保險(xiǎn)人和再保險(xiǎn)人雙方的利益,建立并研究保險(xiǎn)人與再保險(xiǎn)人之間的Stackelberg博弈問題。再保險(xiǎn)人由于其雄厚的資本和較強(qiáng)的抗風(fēng)險(xiǎn)能力處于博弈中領(lǐng)導(dǎo)者的地位,而保險(xiǎn)人則只能作為追隨者。我們將在最大化期望指數(shù)效用這樣一個(gè)目標(biāo)函數(shù)下考慮博弈問題并通過求解兩個(gè)相聯(lián)系的HJB方程得到相應(yīng)的最優(yōu)策略。(4)延續(xù)上一章的討論,我們將在金融理論中另外一個(gè)被廣泛應(yīng)用的模型:均值-方差模型下研究Stackelberg博弈中保險(xiǎn)人和再保險(xiǎn)人的最優(yōu)均衡策略。由于模型的目標(biāo)函數(shù)無法寫成一個(gè)關(guān)于終端變量或財(cái)富函數(shù)的期望,貝爾曼最優(yōu)化原理并不成立,也使得我們?cè)诮鉀Q這類問題時(shí)無法應(yīng)用一般的動(dòng)態(tài)規(guī)劃準(zhǔn)則去推導(dǎo)HJB方程。我們會(huì)應(yīng)用Bjork and Murgoci[16]中的理論去解決這樣的時(shí)間不一致問題并通過兩個(gè)廣義HJB方程的求解而得到相關(guān)的均衡策略。在這一章中我們將分別考慮比例再保險(xiǎn)和超額損失再保險(xiǎn)兩種再保險(xiǎn)形式。本文的結(jié)論與成果豐富了最優(yōu)投資再保險(xiǎn)問題的研究,有助于保險(xiǎn)人和再保險(xiǎn)人分析和選擇相關(guān)的投資再保險(xiǎn)策略。
[Abstract]:As an integral part of the market economy, insurance companies obtain premium and provide financial protection by selling insurance policies to individuals and collectives. For the profit insurer, the insurer can invest it in the financial market and obtain greater returns by buying stock bonds. A risk company sometimes needs to transfer some of its insurance risks and benefits to the reinsurance company, that is, to pay a certain amount of reinsurance for the reinsurance company to take on a part of the insurance risk loss. In such a process, a self born question is how to choose the amount of the investment stock and bond and the purchase. The number and type of reinsurance. We attribute such a kind of problem to the optimal investment reinsurance problem. This paper studies the related problems of the optimal investment reinsurance strategy under different models. The main work is as follows: (1) for the more generalized two segment utility function model, we discuss the related optimal investment in the second chapter. Based on the martingale theory and the method of convex optimization, we transform the original dynamic optimization problem into a solution to a static optimization problem. We obtain the related conditional expectation by the form of the terminal variables obtained, and then obtain the optimal investment reinsurance strategy after comparison. In addition, we give the results. The optimal strategies for several common utility functions are found in the form. (2) for the insurance companies of financial insurance, the principle of variance premiums has more extensive application and practical significance. In the third chapter, we will consider the optimal investment reinsurance problem of the insurer under the principle of variance premium in order to better describe the changes in the market. A continuous time Markov chain is used to describe the variation of the model parameters, that is, the classical Regime-Switching model, and the optimal strategy under two different risk models is considered. In addition, we also restrict the amount of the insurer to invest in the stock market and the amount of the reinsurance that can be purchased, making our model more useful. There are practical significance. (3) in the past, most of the best reinsurance problems are considered based on the perspective of the insurer. In the literature, the best reinsurance problem is considered from the angle of reinsurance or the angle of both parties. However, as a reinsurance contract jointly formulated by both the insurer and the reinsurance person, only the insurance is considered. A person's angle is incomplete in a sense. In other words, a reinsurance contract only considering the interests of any party may not be accepted by the other party. In the fourth chapter, we will take into account the interests of both the insurer and the reinsurance party, and establish and study the Stackelberg game between the insurer and the reinsurance person. People are in the position of leaders in the game because of their strong capital and strong anti risk ability, and the insurer can only be the followers. We will consider the game problem under the objective function of maximizing the expectation index utility and obtain the corresponding optimal strategy by solving the two HJB equation. (4) continuation of the last chapter We will study the optimal equilibrium strategy of the insurer and reinsurance in the Stackelberg game under the mean variance model in the financial theory, which is widely used in the financial theory. Because the objective function of the model can not be written as a expectation of the terminal variable or the wealth function, the Behrman optimization principle is not set up. We can not apply the general dynamic programming criterion to deduce the HJB equation when solving these problems. We will apply the theory of Bjork and Murgoci[16] to solve such a time inconsistency problem and get the related equilibrium strategy by solving two generalized HJB equations. In this chapter, we will consider the proportional reinsurance respectively. The conclusions and results of this paper enrich the research on the problem of optimal investment reinsurance, which will help the insurers and reinsurers to analyze and select related investment reinsurance strategies. The results and results of this paper are two reinsurance forms.

【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224;F842.3

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