Mentor: Dr. Leslie Cheng
This summer, I will be doing research with Professor Leslie Cheng as my adviser. My research will focus on financial mathematics and harmonic analysis. Because I am an A.B./M.A. student in mathematics, this experience may later provide me with a topic to explore for my master's thesis.
The first part of my research focuses on financial mathematics. Financial mathematics is concerned with calculating how much one should pay for financial securities like stocks, bonds, and options, and finding what combinations of the securities make the best investment. An option is the right to buy or sell an asset or a stock. I will focus on lookback options, a type of exotic option that pays the option buyer the maximum value of the stock over time at a specified expiration date. By completing background reading from previous financial mathematics lectures, I will try to modify the Black-Scholes Formula for European call options.
The second part of my research focuses on harmonic analysis. The purpose of harmonic analysis is to examine mathematical objects by decomposing them into simple building blocks. Some applications of harmonic analysis are fingerprint compression, object detection, and audio denoising. I will assist Professor Cheng and Professor Rhonda Hughes, who intend to write an introductory text on harmonic analysis and wavelets for students with only a calculus and linear algebra background. The book will be based on lecture notes from the Math 361 Introduction to Harmonic Analysis and Wavelets course that I took this past spring semester. As part of the project, I will learn a computer program called LaTex, which will be helpful when writing my thesis. Also, I will attend harmonic analysis seminars about oscillatory integrals, which Professor Cheng will run.