本文選題：CEV模型 + 資產(chǎn)-負(fù)債管理��； 參考：《工程數(shù)學(xué)學(xué)報(bào)》2014年01期

【摘要】：本文研究CEV模型下基于效用最大化的資產(chǎn)-負(fù)債管理問(wèn)題.文章假設(shè)股票價(jià)格服從CEV模型,而負(fù)債服從帶漂移的布朗運(yùn)動(dòng),且與股票價(jià)格存在一般相關(guān)性.應(yīng)用動(dòng)態(tài)規(guī)劃原理得到值函數(shù)滿足的HJB方程,并應(yīng)用Legendre變換-對(duì)偶方法得到其對(duì)偶方程.假設(shè)投資人對(duì)風(fēng)險(xiǎn)的偏好滿足二次效用函數(shù),并應(yīng)用變量替換方法得到最優(yōu)投資組合的閉式解.結(jié)果表明:最優(yōu)投資組合包含一個(gè)修正因子,該修正因子可影響投資人為對(duì)沖波動(dòng)率風(fēng)險(xiǎn)而作出的投資決策.最后,文章分析了修正因子的性質(zhì)并考察了修正因子對(duì)最優(yōu)投資組合的影響.
[Abstract]:In this paper, we study the asset-liability management problem based on utility maximization in CEV model. This paper assumes that the stock price service follows the CEV model, while the debt service follows the Brownian motion with drift, and there is a general correlation between the stock price and the stock price. The HJB equation satisfying the value function is obtained by using the principle of dynamic programming, and the dual equation is obtained by using Legendre transform duality method. It is assumed that the investor's preference for risk satisfies the quadratic utility function, and the closed-form solution of the optimal portfolio is obtained by using the variable substitution method. The results show that the optimal portfolio contains a correction factor which can affect the investment decisions made by investors to hedge volatility risk. Finally, the properties of the correction factor are analyzed and the influence of the correction factor on the optimal portfolio is investigated.
【作者單位】： 天津工業(yè)大學(xué)數(shù)學(xué)系;天津大學(xué)管理學(xué)院;天津大學(xué)理學(xué)院;
【基金】：The Humanities and Social Science Research Youth Foundation of Ministry of Education(11YJC790006) the Higher School Science and Technology Development Foundation of Tianjin(20100821)
【分類號(hào)】：F830.59;F224

【共引文獻(xiàn)】

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2 王秀國(guó);王義東;;基于隨機(jī)基準(zhǔn)的動(dòng)態(tài)均值-方差投資組合選擇[J];控制與決策;2014年03期

3 劉利敏;肖慶憲;;不允許賣空限制下跳-擴(kuò)散模型的均值-方差策略選擇[J];數(shù)理統(tǒng)計(jì)與管理;2014年01期

4 朱懷念;植t熀，

本文編號(hào)：2064065