Knight不确定及机制转换环境下带通胀的投资问题研究

发布时间：2018-11-21 14:42

【摘要】：最优消费和投资策略问题一直是金融数学的基本问题之一,受到国内外研究者的广泛关注。早期最优投资消费问题的研究是在完备的金融市场假设下建立最优投资策略模型。近些年来,研究者在此基础上考虑了决策者的信仰、Knight不确定及机制转换等因素对投资策略的影响,使得投资策略的理论建模更加符合当今经济现状。考虑到大多数情况下不确定性不等同于风险。不确定性对收益所带来的影响往往在很大程度上高于风险所带来的影响,为了完善投资决策模型,我们将Knight不确定性研究在内。另一方面,根据已有的研究成果,我们可以看出机制转换环境对决策收益也存在一定的影响。因此将机制转换环境引入最优投资消费决策问题的研究中。而通过对已有经济数据的分析,我们不难发现,在现实经济环境中通货膨胀或通货紧缩、红利支付及汇率变动对投资决策都存在一定程度的影响。因此,我们在研究Knight不确定性及机制转换对投资策略影响的基础上加入考虑通胀因素、红利支付及汇率变动,建立符合经济现状的投资策略模型,可以为投资者提供更为有效的理论分析依据。文章研究了投资者在Knight不确定及机制转换环境下分别考虑了红利率、汇率变动及通胀等因素对投资问题的影响。首先,利用Ito公式推导出机制转换环境下利润流的动力学方程。其次,运用α-最大最小预期效用偏好模型刻画了投资期望值。接下来再利用随机分析方法推导出Knight不确定及机制转换条件下考虑通胀因素的投资预期价值公式和利润流临界现值、推导出标的股票在机制转换市场环境下期权的估值公式、奈特不确定及机制转换环境下考虑汇率变动的项目预期价值公式及利润流临界现值。最后对结果进行了数值模拟,分析了不同参数对投资的影响,即同时考虑Knight不确定、机制转换、红利率、汇率、通胀率以及通胀变化率对投资决策的影响,完善投资决策模型。
[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 伪-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.
【学位授予单位】：安徽工程大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.59;F820.5;F224

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