MATH 7380-3: Applied Stochastics

Place: Lockett 132
Time: Mon Wed Fri 1:40pm to 2:30pm

Instructor: Dr. Ambar Sengupta
Office: Lockett 324
Telephone: 225-578-1607

  • Prerequisite: Math 7311 Real Analysis I and elementary probability theory
  • Course Material: Notes will be provided; books will be recommended.
  • This course will cover topics in stochastic analysis with a view towards applications in finance. In the first few weeks we will go over the basic framework of probability theory (probability spaces, random variables) and essential tools. We will then study Brownian motion and other stochastic processes, examining the beautiful and surprising relationship between such processed and partial differential equations. A typical question of interest is: how long does it take for a random process to escape from a given region? In this context we will study the Feynman-Kac formula, which arose in physics but has application in finance.

    On the financial side, we will see a very simple approach to the celebrated Black-Scholes-Merton formula for pricing stock options. We will examine the structure of certain financial products such as bond options, swaps, and credit derivatives. Pricing and risk management of these derivatives will be examined. Credit derivatives form a currently highly active area both in the "real world" of finance and in development of the theory.