本文選題：對(duì)偶模型 + 周期性分紅�。� 參考：《湘潭大學(xué)》2017年碩士論文

【摘要】：該文主要在有界紅利率的條件下討論復(fù)合二項(xiàng)對(duì)偶模型的周期性分紅問(wèn)題。通過(guò)對(duì)值函數(shù)進(jìn)行變換,得到了最優(yōu)紅利策略的一些性質(zhì),并且證明了最優(yōu)值函數(shù)是一個(gè)HJB方程的唯一解。從而得到了最優(yōu)策略和最優(yōu)值函數(shù)的一個(gè)簡(jiǎn)單計(jì)算方法。根據(jù)最優(yōu)紅利策略的一些性質(zhì),該文還得到了最優(yōu)值函數(shù)的可無(wú)限逼近的上界和下界。最后提供一些數(shù)值計(jì)算實(shí)例來(lái)說(shuō)明該算法。該文主要內(nèi)容如下:第二章介紹了基本模型和給出最優(yōu)控制問(wèn)題的一個(gè)嚴(yán)格數(shù)學(xué)表達(dá)。第三章給出了最優(yōu)值函數(shù)的HJB方程,得到了最優(yōu)分紅策略的一些性質(zhì)。第四章通過(guò)最優(yōu)紅利策略的一些性質(zhì)得到了最優(yōu)值函數(shù)的可無(wú)限逼近的上界和下界,并通過(guò)幾個(gè)數(shù)值計(jì)算實(shí)例來(lái)說(shuō)明該算法。
[Abstract]:In this paper, we discuss the periodic dividend of compound binomial duality model under the condition of bounded red interest rate. By transforming the value function, some properties of the optimal dividend strategy are obtained, and it is proved that the optimal value function is the unique solution of a HJB equation. A simple calculation method of optimal strategy and optimal value function is obtained. According to some properties of optimal dividend strategy, the upper bound and lower bound of infinite approximation of optimal value function are also obtained. Finally, some numerical examples are provided to illustrate the algorithm. The main contents of this paper are as follows: in chapter 2, we introduce the basic model and give a strict mathematical representation of the optimal control problem. In chapter 3, we give the HJB equation of the optimal value function and obtain some properties of the optimal dividend policy. In chapter 4, we obtain the upper bound and lower bound of infinite approximation of optimal value function by some properties of optimal dividend strategy, and illustrate the algorithm by several numerical examples.
【學(xué)位授予單位】：湘潭大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 劉偉;袁海麗;胡亦鈞;;THE OPTIMAL STRATEGY FOR INSURANCE COMPANY UNDER THE INFLUENCE OF TERMINAL VALUE[J];Acta Mathematica Scientia;2011年03期

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本文編號(hào)：2099781