金融数学专业课题:市场优化与风险机制设计及分析
Introduction to Financial Mathematics
课题海报
Course Arrangement
课程安排
课程时间:全年滚动招生
课程形式:远程线上授课
课时安排:37.5课时教授授课与科研论文指导+15课时副导师论文辅导&不限次数润色修改+16课时论文写作课
Subject Background
背景
课程背景
自20世纪90年代以来,数学、金融、计算机及经济呈现融合趋势。货币市场每天的交易量达到2万亿美元,诸如期权、互换、交叉货币证券等复杂金融工具的交易非常普遍。可以讲,自1973年Black-Scholes公式出现以来,金融界被大量丰富的数学工具和模型所包围。21世纪金融数学领域如Kurzweil加速回报率所描述的那样增长更为迅速,从业人士们也开始运用金融数学的思考模式对大量的市场交易活动进行应用分析。
课程目标
金融数学作为一个重要的,涉及着在金融领域设计和分析各种产品,旨在提高市场效率并建立降低风险的机制。本课程深入介绍了这些现代概念和定量金融的计算技术。主题包括债券市场的基本结构,如收益率曲线和利率期限结构、套利的数学公式和基于无套利的定价技术、Cox-Ross-Rubinstein的经典二项式模型、广泛使用的Black-Scholes公式、历史波动率和隐含波动率以及动态编程。还讨论了许多实用的金融工具,如虚值看涨期权和看跌期权,以及欧式期权、美式期权和障碍期权之间的区别。
Course background
Since the 1990s, there has been a trend of convergence among mathematics, finance, computer science, and the global economy. The daily trading volume in the currency market reaches two trillion dollars, and transactions involving complex financial instruments such as options, swaps, and cross-currency securities have become widespread. It can be said that since the emergence of the Black-Scholes formula in 1973. the financial industry has been surrounded by a wealth of mathematical tools and models. In the 21st century, the field of financial mathematics has grown even more rapidly, as described by Kurzweil's accelerating returns, and professionals have begun applying the mindset of financial mathematics to analyze a plethora of market trading activities.
Course objective
Financial Mathematics is concerned with designing and analyzing products that improve the efficiency of the markets and create mechanisms for reducing risk. This course provides an in-depth introduction to these modern concepts and the computational techniques in quantitative finance. Topics include the basic structures of the bond markets such as the yield curve and the term structure of interest rates, mathematical formulation of arbitrage and pricing techniques based on no-arbitrage, classical binomial model of Cox-Ross-Rubinstein, widely used Black-Scholes formula, historical and implied volatility and and the dynamic programming. Many practical financial instruments such as vanilla call and put options, differences between European, American and barrier options are discussed.
Suitable For
适合人群
对金融数学感兴趣,特别是希望深入了解时间价值、金融工具、期货交易、衍生品定价、金融模型以及Python编程在金融领域的应用的学生。
修读金融学、金融工程、会计、数学、计算机科学、统计学等相关专业,以及未来希望从事于金融分析、投资银行、金融衍生品交易、风险管理等领域的学生。
Professor Introduction
导师介绍
Mete Soner
普林斯顿大学终身教授
普林斯顿大学运筹学和金融工程学终身教授
普林斯顿大学Bendheim金融中心项目成员
曾担任苏黎世联邦理工学院数学系主任
前苏黎世联邦理工学院数学系终身教授
曾任职于美国和欧洲多所大学,包括CMU, ETH等
SIAM Journal of Financial Mathematics主编
《数学与金融经济学》联合主编
2014年荣获“洪堡研究奖”
专业期刊论文引用次数18763次; h指数: 58; i10: 119
研究方向 Research Interests
Stochastic Optimal Control 随机较优控制
Markov Decision Processes
马尔科夫决策过程
Nonlinear Partial Differential Equations
非线性偏微分方程
Probability Theory 概率论
Mathematical Finance 数学金融
Financial Economics 金融经济学
Student Papers
往期学员论文
The Analysis of Financial Crisis in 2008
2008年金融危机的分析
Quasi-sure Stochastic Analysis through Aggregation
通过聚集进行准增加的随机分析
Martingale Optimal Transport and Robust Hedging in Continuous Time
连续时间内的马丁格尔较优运输和稳健对冲
Instructor Team
师资配置
教授
世界名校教授,为学员量身定制课题方向,亲自授课并指导科研与论文
副导师
名校硕博研究生,针对学员需求个性化课题辅导,不限次数论文润色修改
班主任
标准化流程一对一服务跟进,全程增加学员的项目体验
Program System
项目设置
Learning Outcomes
学习成果
Other Information
其他资料
MeteSoner_CV.pdf
相关论文.pdf
录取案例.pdf
论文常见问题.pdf