考虑通货膨胀因素影响下的最优消费投资策略研究
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考虑通货膨胀因素影响下的最优消费投资策略研究(论文10000字)
摘要：在金融数学中，运用数学知识推理特定情况下的最优消费投资模型现已是一个重点的研究方向。最优消费投资策略指的是投资人如何在消费与投资之间平衡自己的已有资产。为了能够创建最能适合于实际的最优消费投资模型，本文首先运用了 创建的消费投资组合模型作为理论基础，以及能够体现实际的约束条件，同时还顾及到通货膨胀对投资消费市场的影响程度。
首先，本文将目前国内外的消费投资组合理论的发展情况及现状简明扼要地一一论述，我们可以从中发现在哪些地方存在可以深入探讨的地方；其次，简要地将本文研究所需要的所有重要的理论知识一一介绍，并讲解在何处会用到，如何将其运用等；然后，本论文在资产价格模型的基础上建立了最优消费投资模型，利用伊藤公式及 方程等方法求出模型的解.并且探讨了两种不同风险厌恶情况的消费投资模型并最终求出了符合最佳策略的解；最后，以人寿保险为研究内容，在考虑通胀的条件下研究包含人寿保险的最优投资策略。本文得到的结论是：通货膨胀和投资人最终的投资收益是息息相关的，如果通货膨胀的变化趋势和市场风险证券的变化趋势呈现负向的关系时，我们需要加大在市场风险证券上的投资额来解决通货膨胀的负面影响。
关键词：通货膨胀；最优投资消费模型；伊藤公式； 方程
The optimal consumption and investment strategy under the influence of inflation
Abstract:The optimal consumption investment model using mathematical knowledge reasoning is now a main research direction in financial mathematics.Optimal consumption investment strategy refers to how investors balance their existing assets between consumption and investment. In order to be able to create the most suitable for the actual optimal consumption investment model, this paper first USES to create consumer portfolio model as the theoretical basis, and the ability to reflect the actual constraints, but also consider the impact of inflation on financial markets.
First of all, this paper will be the development of the consumption of portfolio theory at home and abroad, and the present situation briefly discussed one by one;Secondly, it briefly introduces all the important theoretical knowledge needed by this paper, and explains where it will be used and how to apply it.Then, based on the asset price model, this paper establishes the optimal consumption investment model, and uses the ITO formula and equation to find the solution of the model, and we discuss two kinds of consumption investment models with different risk aversion and finally find out the solution that accords with the best strategy.Finally, the optimal investment strategy including life insurance is studied under the conditions of inflation. In this paper, the conclusion is: inflation and the ultimate return on investment is closely linked, and if the change trend of inflation and the change trend of securities market risk is a negative relationship, we need to increase the market risk of securities investment to solve the negative effects of inflation.
Key words: inflation; optimal investment and consumption portfolio model; ITO formula; equation
目 录
1 绪论 1
1.1 现代投资组合理论的背景及研究意义 1
1.2 现代投资组合理论的研究现状 1
1.3 通货膨胀对金融市场的影响 2
1.4 本文主要内容安排 2
2 基本概念及理论知识 2
2.1 效用函数 2
2.2 布朗运动 3
2.3 伊藤公式 4
2.4 随机控制 5
2.5 通货膨胀 6
3 通货膨胀影响下的最优消费和投资组合策略 6
3.1 问题阐述及建立模型 6
3.2 模型求解 8
4 不同效用函数情形下的显式解 10
4.1 常数相对风险厌恶效用函数 11
4.2 绝对风险厌恶效用函数 16
5 通货膨胀影响下的含人寿保险的最优投资策略 21
5.1 问题阐述及建立模型 21
5.2 模型求解 23
6 总结 24
参考文献 25
致谢 26