【摘要】：最優(yōu)消費(fèi)和投資策略問題一直是金融數(shù)學(xué)的基本問題之一,受到國內(nèi)外研究者的廣泛關(guān)注。早期最優(yōu)投資消費(fèi)問題的研究是在完備的金融市場假設(shè)下建立最優(yōu)投資策略模型。近些年來,研究者在此基礎(chǔ)上考慮了決策者的信仰、Knight不確定及機(jī)制轉(zhuǎn)換等因素對投資策略的影響,使得投資策略的理論建模更加符合當(dāng)今經(jīng)濟(jì)現(xiàn)狀。 考慮到大多數(shù)情況下不確定性不等同于風(fēng)險。不確定性對收益所帶來的影響往往在很大程度上高于風(fēng)險所帶來的影響,為了完善投資決策模型,我們將Knight不確定性研究在內(nèi)。另一方面,根據(jù)已有的研究成果,我們可以看出機(jī)制轉(zhuǎn)換環(huán)境對決策收益也存在一定的影響。因此將機(jī)制轉(zhuǎn)換環(huán)境引入最優(yōu)投資消費(fèi)決策問題的研究中。而通過對已有經(jīng)濟(jì)數(shù)據(jù)的分析,我們不難發(fā)現(xiàn),在現(xiàn)實經(jīng)濟(jì)環(huán)境中通貨膨脹或通貨緊縮、紅利支付及匯率變動對投資決策都存在一定程度的影響。因此,我們在研究Knight不確定性及機(jī)制轉(zhuǎn)換對投資策略影響的基礎(chǔ)上加入考慮通脹因素、紅利支付及匯率變動,建立符合經(jīng)濟(jì)現(xiàn)狀的投資策略模型,可以為投資者提供更為有效的理論分析依據(jù)。 文章研究了投資者在Knight不確定及機(jī)制轉(zhuǎn)換環(huán)境下分別考慮了紅利率、匯率變動及通脹等因素對投資問題的影響。首先,利用Ito公式推導(dǎo)出機(jī)制轉(zhuǎn)換環(huán)境下利潤流的動力學(xué)方程。其次,運(yùn)用α-最大最小預(yù)期效用偏好模型刻畫了投資期望值。接下來再利用隨機(jī)分析方法推導(dǎo)出Knight不確定及機(jī)制轉(zhuǎn)換條件下考慮通脹因素的投資預(yù)期價值公式和利潤流臨界現(xiàn)值、推導(dǎo)出標(biāo)的股票在機(jī)制轉(zhuǎn)換市場環(huán)境下期權(quán)的估值公式、奈特不確定及機(jī)制轉(zhuǎn)換環(huán)境下考慮匯率變動的項目預(yù)期價值公式及利潤流臨界現(xiàn)值。最后對結(jié)果進(jìn)行了數(shù)值模擬,分析了不同參數(shù)對投資的影響,即同時考慮Knight不確定、機(jī)制轉(zhuǎn)換、紅利率、匯率、通脹率以及通脹變化率對投資決策的影響,完善投資決策模型。
[Abstract]:The problem of optimal consumption and investment strategy has been one of the basic problems in financial mathematics. The study of the early optimal investment and consumption problem is to establish the optimal investment strategy model under the complete financial market hypothesis. In recent years, on this basis, researchers have considered the influence of the belief of decision makers, the uncertainty of Knight and the transformation of mechanism on the investment strategy, which makes the theoretical modeling of investment strategy more in line with the current economic situation. Considering that in most cases uncertainty is not equal to risk. The influence of uncertainty on income is often higher than that of risk. In order to perfect the investment decision model, we study the uncertainty of Knight. On the other hand, according to the existing research results, we can see that the mechanism transformation environment also has a certain impact on the decision-making income. Therefore, the mechanism-changing environment is introduced into the study of optimal investment-consumption decision-making. Through the analysis of the existing economic data, it is not difficult to find that inflation or deflation, dividend payment and exchange rate change have a certain degree of influence on investment decision-making in the real economic environment. Therefore, on the basis of studying the influence of Knight uncertainty and mechanism transformation on investment strategy, we add inflation factor, dividend payment and exchange rate change into consideration, and establish an investment strategy model that accords with the current economic situation. It can provide more effective theoretical basis for investors. In this paper, the investors' influence on the investment problem is studied under the environment of Knight uncertainty and mechanism transition, including red interest rate, exchange rate change and inflation. Firstly, the dynamic equation of profit flow in the environment of mechanism conversion is derived by using Ito formula. Secondly, the expected value of investment is described by 偽-maximum and minimum expected utility preference model. Then, by using the stochastic analysis method, the paper deduces the expected investment value formula and the critical present value of profit flow under the condition of Knight uncertainty and mechanism conversion, and deduces the valuation formula of the stock option under the market environment of mechanism conversion. The formula of expected value and the critical present value of profit flow considering exchange rate change under Knight uncertainty and mechanism transition environment. Finally, the effects of different parameters on investment are analyzed, including Knight uncertainty, mechanism transformation, red interest rate, exchange rate, inflation rate and inflation rate.
【學(xué)位授予單位】：安徽工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F830.59;F820.5;F224

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