*Math 590 Financial Engineering
*

or Mathematics of Stock Markets

Fall 1996

*Syllabus*

**Time Table:**
Time=11MWF Room=316TH Call=61738 Instructor=Lipton

**Outline:**
This is an introduction into a rapidly developing area of mathematics
known as financial engineering. Recent advances in understanding the
behavior of the bond and stock markets will be described from a
mathematical viewpoint. Modern financial instruments and mathematical
methods of their valuation will be discussed in detail. Hands on
experience in numerical methods will be provided.

**Instructor:**
Alexander Lipton (Lifschitz), 728 SEO, 996-4609, alexli@uic.edu

**Office Hours:**
M, W, F 12PM or by appointment

**Instructor Web Page:** http://www.math.uic.edu/~hanson/lipton.index.html

**Prerequisites:**
Graduate standing and Math 481 Applied Partial Differential Equations
and MCS 471 Numerical Analysis or consent of the instructor

**Grading:**
Grade will be based on homework and computer problems to be distributed
during the semester; there will be no exams

**Texts:**
- P.W. Wilmott, S. Howison, J. Dewynne,
*The Mathematics of Financial Derivatives: a Student Introduction,*
Cambridge Univ Press, 1995
- J. Hull,
*Options, Futures, and Other Derivative Securities,*
Prentice-Hall, 1993.
- G.D. Smith, Numerical Solution of Partial Differential Equations,
3rd edition, Oxford Univ Press, 1985.
- A.J. Davies, The Finite Element Method: A First Approach,
Oxford Univ Press, 1986.

**List of Topics:**
*Numerical Methods for Parabolic PDEs:* review of finite difference
methods, explicit methods, Crank-Nicolson implicit method,
consistency, stability, convergence, Fourier stability methods,
alternating directions implicit method, higher
level schemes, nonlinear equations, predictor corrector methods,
trees, lattice methods, Monte-Carlo methods, computer problems, 12 hours
*Stochastic Processes:* basic concepts, elements of random
analysis, infinite-dimensional distributions, martingales, Markov
processes with discrete time, Marcov processes with continuous
time, stochastic equations and diffusion, computer problems, 12 hours.
*Financial Derivatives:* overview of stock and bond markets,
the Black-Scholes models, risk neutral pricing,
basic options, European, American, Asian, barrier, and exotic
options, free-boundary versus fixed-boundary problems, interest
rate derivatives, computer problems, 15 hours.
*Special topics:* implied volatilities, the volatility smile,
chaos, nonlinear dynamics and neural networks, computer problems,
6 hours.

`Web Source: http://www.math.uic.edu/~hanson/math590f96syllabus.html`