MATH 5709-0

Brief

Financial Mathematics is a pivotal field that employs mathematical methodologies to address real-world financial challenges. This course is designed to provide students with the essential tools and skills necessary for understanding and analyzing financial instruments, risk management, investment strategies, and decision-making processes in finance. Throughout the course, students will build a robust foundation in mathematical finance and explore its practical applications in diverse financial settings.

Description

Course keywords: Optimization, Control Theory, Stochastic Process, Reinforcement Learning, Financial Machine Learning Course Overview: This course focuses on optimization and control problems in finance, covering areas such as portfolio construction, execution, market making, and hedging. The methodological approach will be adapted based on students' background and preferences. Course Options: Option 1: Discrete Approach Key Topics: Markov Decision Process, Control & Optimization, Reinforcement Learning Advantages: Access to numerous numerical algorithms and thus huge potential for real- world application. Challenges: Difficulty in achieving theoretically optimal solutions. Prerequisites: Proficiency in linear algebra and probability. Knowledge of Python coding is beneficial. Option 2: Continuous Approach Key Topics: Stochastic Process, Stochastic Portfolio Theory, Stochastic Control & Optimal Stopping Advantages: Utilizes a broad range of mathematical tools for comprehensive analysis. Challenges: Complexities in applying these theories to real-world situations. Prerequisites: Background in real analysis, probability, and ODE&PDE is essential. Option 3: Financial Machine Learning Key Topics: Financial Data Analysis, Modelling, Backtesting, & Financial Features. Advantages: Represent a mainstream methodology widely adopted by hedge fund practitioners. Challenges: Necessitate substantial domain expertise for the development of effective intuition. Prerequisites: A foundation in statistics, probability, and machine (statistical) learning is necessary for this course. Course Duration: 16 weeks Evaluation: 100% Project-based - Participants will choose their preferred project and methodology at the beginning of the semester. Together, we will formulate a realistic and effective learning plan. - During the semester, each group must provide regular presentations on their project. These presentations should include background knowledge, theoretical techniques, and the implementation algorithms used. - The final report, to be submitted in Markdown format, should feature clean code and well- structured details. It will be published online for assessment.

Timetable

Scores

Average GPA 3.21

Std. Deviation 1.12

Remarks

X-Class,金融數學需要會微積分/線性代數/機率。本課程上150分鐘，其餘時間由教授彈性運用。

Restrictions

Compulsory

Elective

Cross Discipline

First Specialization

Second Specialization