Current Teaching

Spring 2023:  On sabbatical leave 

Recently developed courses

Quantitative Risk Management (Math 588, Illinois Tech) 

 The course covers the major concepts and ideas from the modern risk management . It builds upon general theory of risk measures and performance measures and addresses the current regulatory requirements for market participants.  

Significant part of the course will be devoted to practical aspects of the risk management, including: working with real market data, implementing the theoretical concepts by developing Python libraries that perform a comprehensive risk analysis of portfolios of various financial instruments.  

The course should be accessible to students with knowledgeable of general probability (Math 475) and elements of financial markets (Math 548 or Math 485). 

Course Plan: 

1. Basic concepts in risk management

2. Modeling portfolio value and its change

3. Theory of risk and performance measures

4. Applications to Market risk and Credit Risk

5. Central Clearing Counterparties (CCP)

Textbook: Alexander J. McNeil, RÃijdiger Frey & Paul Embrechts, Quantitative Risk Management Concepts, Techniques and Tools, Princeton University Press, First Revised Edition, 2015, ISBN-13: 9781400873210 .

Course Materials: Lecture Notes (for registered students only). All materials will be posted on the BlackBoard.

Stochastic Partial Differential Equations (Math 545, Illinois Tech)

This course aims to give a fair introduction to general theory of Stochastic Partial Differential Equations (SPDEs), and their applications to various areas of applied mathematics. Starting with simple  examples of SPDEs, such as stochastic heat equation, the courses advances to general theory of existence, uniqueness and regularity of the solutions for a SPDEs (mainly parabolic). In the second part of the course, students will learn fundamentals of statistical analysis for stochastic processes with main focus on parameters estimation problems for parabolic SPDEs. 

The course is designed for graduate students with general research interests in stochastic methods.  Students are expected to have some basic knowledge of PDEs and stochastic calculus. 

Course Plan: 

1. Prelimenaries

2. Examples of SPDEs based on applications

3. Stochastic Parabolic Equations

4. Numerical Solutions for SPDE

5. Statistical Inference for SPDEs

Textbook: S. V. Lototsky and B. L. Rozovsky, Stochastic Partial Differential Equations, Springer (2017), ISBN 978-3-319-58647-2.

Courses taught at Illinois Tech


Courses taught at University of Moldova