微积分在金融投资中的应用

摘  要

微积分与数学是有着十分密切关系的两个学科，微积分中的很多金融投资现象金融投资理论都能够用数学知识去解释。现代化金融投资理论已经从过去的金融投资定性分析发展成为量性分析和定性分析相结合。微积分作为数学知识的基础，是学习金融投资学的必备知识，在这里我要介绍一下微积分知识在金融投资学中的一些基本的应用。微积分在金融投资领域中的应用，主要是研究在这一领域中出现的一些函数关系，因此必须了解一些金融投资分析中常见的函数。价格函数、需求函数、成本函数、收益函数等等。还有弹性的金融投资分析，需求弹性、收益弹性等等。最优化问题是金融投资管理活动的核心，各种最优化问题也是微积分中最关心的问题之一。这些重要的金融投资理论都可以用微积分的一些内容解释，所以说微积分在金融投资学中的应用是十分有效的。

关键词：微积分；金融；投资；应用

ABSTRACT

Calculus and mathematics are two subjects which have a very close relationship. Many financial investment phenomena in calculus can be explained by mathematical knowledge. Modern financial investment theory has developed from qualitative analysis of financial investment to quantitative analysis and qualitative analysis. As the basis of mathematical knowledge，calculus is the necessary knowledge to study financial investment. Here I want to introduce some basic applications of calculus in financial investment. The application of calculus in the field of financial investment is mainly to study some functional relations that appear in this field，so it is necessary to understand some financial investment analysis. Functions common in the. Price function，demand function，cost function，income function，etc. There are also flexible financial investment analysis，demand elasticity，income elasticity and so on. Optimization is the core of financial investment management，and various optimization problems are also one of the most concerned problems in calculus. These important financial investment theories can be explained by calculus，so the application of calculus in financial investment is very effective.

Key words: calculus; finance; investment; application

目  录

摘  要I

ABSTRACTII

1绪论1

1.1选题背景及意义1

1.2国内外研究现状1

1.3微积分发展概述2

1.3.1微积分学的创立2

1.3.2微积分诞生的重要意义3

1.3.3微积分理论内容介绍3

1.3研究主要内容4

2微积分在金融投资中的应用5

2.1导数在金融投资中的应用5

2.1.1导数在金融投资边际分析部分的应用5

2.1.2导数在弹性理论中的应用11

2.2极限在金融投资中的应用14

2.2.1极限解决连续复利问题14

2.2.2极限在弹性求法中的应用15

2.3积分在金融投资中的应用15

2.3.1利用积分性质用来求原函数16

2.3.2利用积分性质计算消费者剩余16

3总结19

参考文献20