金融数学

学分：6

本课程将通过连续时间方法剖析金融衍生品问题，讲述各种问题中的相关偏微分方程式和边界条件；结合使用多种分析法和计算法探索解题方法；分析一系列离散时间金融模型，主要包括（但不限于）资产收益及其波动性、两种资产和多种资产组合投资优化及多种投

资模型（如期权、期货、债券）等。

在本课程结课时，学生应能够：

• 写出各种金融衍生品问题中的偏微分控制方程式和边界条件

• 在某些金融衍生品问题研究过程中运用多种分析法和计算法解答相关偏微分控制方程式

• 表达自己对数学（尤其是离散数学概念）如何用于经济领域金融部门的理解

• 表达自己对计息办法、资产收益和投资类型的理解，如债券、期货和期权；并说明为获得风险最低的收益，如何打造风险性资产投资组合

Introduction to Mathematical Finance 金融数学（可能后续要改成Finance Mathematical）

Credits: 6

Financial derivatives are examined using a continuous-time approach, examining the relevant partial differential equations and boundary conditions in a number of different problems. The solution method is examined, using a mix of analytical and computational methods. A range of discrete time financial models is analysed. This includes mainly(but not exclusively) the return of assets and their volatility, two asset and multi-asset portfolio optimisation and various investment models such as options, futures and  bonds.

By the end of this module, students should be able to:

• Write down the governing partial differential equations and boundary conditions for a range of financial derivative problems

• Solve the relevant partial differential equations arising from the study of some financial derivative problems using analytical and computational methods

• Demonstrate an understanding of how mathematics and in particular discrete mathematics is used in the financial sector of the economy

• Demonstrate an understanding of how interest calculations, asset return and investment types such as bonds, future and options, and of how investment portfolios of risky assets should be composed in order to obtain a desired return with minimum risk

Financial Mathematics（还未有最终翻译的正式版本）

Credits:6

Module Description:

This module introduces the fundamentals of mathematical modelling in finance, and the mathematics of financial annuities and investments.  We explore the use of deterministic models that can be used to model and value known cashflows.  We also explore stochastic, discrete-time models of investment risk and return.

Topics:

Data and financial modelling

Theory of interest rates

Equations of Value

Theories of financial market behaviour

Introduction to interest rate models

Modern portfolio theory

Asset valuation

Measures of investment risk

Module Outcomes:

1. Describe, interpret, and discuss the theories on interest rates.

2. Derive and define constant and time-varying compound interest functions and annuities

3. Define, interpret, and apply an Equation of Value

4. Describe, construct, interpret, and discuss the models underlying asset valuations

5. Discuss the advantages and disadvantages of different measures of investment risk