Yeshiva University, Mathematics

Program ID: 137-REU [#1118]
Program Title: REU in stochastic processes and financial time series
Program Type: Undergraduate program
Program Location: New York, New York 10016, United States [map]
Application Deadline: 2021/04/10 11:59PMhelp popup (posted 2021/03/22, listed until 2021/09/16)
Program Description:    

We are inviting motivated undergraduate students to join our fully online REU program. The program consists of 2 parts. 

1) Undergraduate summer workshop June 1, 2021 - June 11, 2021 

This is a 2-week intense summer workshop on financial time series and stochastic processes. The workshop has daily lectures in three courses. The first course is "Financial Surveillance via Change-Point Detection" by prof. Pablo Roldan. The second course is "Stochastic Interacting Particle Systems" by prof. Peter Nandori. The third course is "Topological Data Analysis of Time Series" by prof. Marian Gidea. See the abstract for each course below. All lectures will be online. Lecture times are 10 am - 11 am, 11:15 am - 12:15 pm, 2 pm - 3 pm Eastern time on every weekday between June 1st and June 11th. 

2) Hands-on research experience for undergraduates 

Motivated students who completed the summer workshop will have the opportunity to join a research projects in one of the topics discussed in the workshop. The research will be carried out during a period of one month following the workshop. A limited number of stipends is available for students participating in the research. 

Application details

Both parts of the program will be entirely online. To apply for the summer workshop, students should have completed one semester of college level probability theory. Preference will be given to students who completed multiple rigorous undergraduate courses in mathematics. The summer workshop is open to current undergraduate students including those who graduate in 2021. Students who want to stay in the second part are required to attend the workshop. Please indicate in your cover letter if you only apply for the first part or both parts. In the second part, stipend eligibility is restricted to only those students who are currently authorized to work in the United States and maintain their undergraduate status throughout the summer. 


Courses in the summer workshop 

  1.  Financial Surveillance via Change-Point Detection The world’s history of economic crises, including the recent COVID-related downturn around March 2020, provides graphic evidence of the importance of efficient methods for continuous financial surveillance toward better active risk management. In this course, we consider the problem of “real-time” detection of crashes in “live”-monitored financial time series. This problem will be approached using statistical time-series analysis. In particular, we will discuss Change-Point Detection methods, which try to identify times when the probability distribution of a stochastic process or time series changes. Our working assumption is that, whenever a financial crash happens, the underlying distribution of the observable time-series changes drastically. In general, the problem concerns both detecting whether a change has occurred (or possibly several changes) and identifying the time when they might have occurred. Of course, we would like to detect these structural breaks efficiently, i.e. as promptly as possible, and without raising many “false alarms”. We plan to 1. Review the most useful Change-Point Detection methods for this particular problem; and 2. Apply them to a concrete financial time-series, such as the evolution of the SP 500 stock index, or the price of Bitcoin. 
  2. Stochastic interacting particle systems On the atomic level, physical materials are quantized yet on the macroscopic level, they look continuous. It is an important challenge in mathematical physics to provide feasible mathematical models for systems that are quantized microscopically but macroscopically obey some basic laws of physics, such as the heat equation. There is a vast scientific literature on this subject, in particular the challenge has been solved for many stochastic microscopic models, also known as stochastic interacting particle systems. In this minicourse, we will present some of these results. In particular, we will focus on one of the simplest techniques which is based on duality of Markov chains. We will also present interesting open problems.
  3. Topological Data Analysis of Time Series Topological Data Analysis (TDA) is a new way to make sense out of complex data, complementary to Statistics. Whereas the statistical approach aims to approximate a data set by a probability density function, the TDA approach describes the data set as a geometric shape, using tools from topology. This course will provide a hands-on introduction to TDA. We will use computer software to analyze time series obtained from both chaotic and stochastic processes. In particular, we will use TDA for early detection of ‘critical transitions’, when the underlying system switches abruptly from one state to another, radically different state. As an application, we will investigate crashes in the financial markets.

Application Materials Required:
Submit the following items online at this website to complete your application:
Further Info:
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