Description:
This course will cover much of Professor Pliska's book Introduction to
Mathematical Finance, which as the name suggests is a theoretical yet
introductory study of security markets including stocks, bonds,
futures, and options. Considerable attention will be given to topics in
financial economics such as arbitrage, risk neutral valuation of
derivative securities, and optimal consumption/investment problems
where the objective is to maximize expected utility. Although the
course will involve mathematics presented in a rigorous fashion, the
only mathematical prerequisites are knowledge about probability,
calculus, linear algebra, and optimization, so economics students who
have completed the first year of graduate study should be well
qualified. No particular courses in finance are prerequisites, but
students should come with an interest in financial markets. Additional
information about the book and the course (which is being taught this
spring) can be found on
Professor Pliska's web page.
COURSE DESCRIPTION:
Finance is one of the fast growing areas in the
corporate world. Along with this, the explosion in financial instruments
has led ot the development of new mathematical models and methods
for their analysis. The course begins with a review of financial
derivatives
and their applications. Models of financial derivatives will be
presented
such as Black-Scholes model. The approach will be baseed on partial
differential equations using analytic and numerical methods.
PREREQUISITES:
Background in differential equations and
introductory probability or consent of the instructor.
TEXT(S):
Wilmot, Howison, and Dewynne, The Mathematics of Financial
Dervatives;
A Student Introduction, Cambridge University Press.
Math 590 Advances Topics in Applied Mathematics:
Computational Finance, Spring 2001, Prof. Charles Tier
TIMETABLE: 62915 LECD 0300-0415 M W 0208 TH
COURSE DESCRIPTION:
Finance is one of the fast growing areas in the
corporate world. Along with this, the explosion in financial instruments
has led ot the development of new mathematical models and methods
for their analysis. The course begins with a review of financial
derivatives
and their applications. Models of financial derivatives will be
presented
such as Black-Scholes model. The approach will be baseed on partial
differential equations using analytic and numerical methods.
PREREQUISITES:
Background in differential equations and
introductory probability or consent of the instructor.
TEXT(S):
Wilmot, Howison, and Dewynne, The Mathematics of Financial
Dervatives;
A Student Introduction, Cambridge University Press.
Math 590 Advanced Topics in Applied Mathematics:
Principles of Financial Mathematics, Spring 2001, Prof. Stephen S. T.
Yau,
TIMETABLE: 62907 LECD 1100-1150 M W F 0303 AH
PREREQUISITES: Approval of the Department. Graduate Standing
Required.
TEXT(S):
S. N. Neftci, An Introduction to the Mathematics of Financial
Derivatives
, Academic Press.
COURSE DESCRIPTION: Continuation of Spring 2000 course that started
with
1. Probability Theory, 2. Financial Instruments, 3. Basic Principles of
Asset Evaluations, 4. One Period Asset Valuation, One Period Pricing
Model,
5. Discrete Time Model, Arbitrage and Martingales, Complete Markets,
6. American Options, Supermartingales and Snell Envelope, Stopping Time,
Decomposition of Supermartingales, 7. Continuous Time Model for Stock
Prices,
Brownian Motion, Continuous Martingale Stochastic Calculus, 8.
Black-Scholes
Differential Equation, The Market Price of Risk.
Description:
This course will cover much of Professor Pliska's book Introduction to
Mathematical Finance, which as the name suggests is a theoretical yet
introductory study of security markets including stocks, bonds,
futures, and options. Considerable attention will be given to topics in
financial economics such as arbitrage, risk neutral valuation of
derivative securities, and optimal consumption/investment problems
where the objective is to maximize expected utility. Although the
course will involve mathematics presented in a rigorous fashion, the
only mathematical prerequisites are knowledge about probability,
calculus, linear algebra, and optimization, so economics students who
have completed the first year of graduate study should be well
qualified. No particular courses in finance are prerequisites, but
students should come with an interest in financial markets. Additional
information about the book and the course (which is being taught this
spring) can be found on
Professor Pliska's web page.
Fin 571 Empirical Issues in Finance. Gilbert W. Bassett, Jr.
Time Table: MW 3:00-4:15, Call Number: 59822
Description:
The course will cover empirical applications focusing on financial
equity data. The course will introduce robust statistical methods,
compare them to standard methods, and present their application to
problems in Finance. Problems to be considered include the
predictability of asset returns, analysis of market microstructure,
multifactor models for predicting returns, risk neutral distributions
implicit in options prices, and forecasting portfolio tracking error.
There will be a required research paper. Students will be assumed to
have taken econometrics and statistical courses at the level of
Economics 534 and 535.
Math 590 Advanced Topics in Applied Mathematics:
Principles of Financial Mathematics, Fall 2000, Prof. Stephen S. T.
Yau,
TIMETABLE: 75266 LECD 1200-1250 M W F 0316 BH
PREREQUISITES: Approval of the Department. Graduate Standing
Required.
TEXT(S):
S. N. Neftci, An Introduction to the Mathematics of Financial
Derivatives
, Academic Press.
COURSE DESCRIPTION: Continuation of Spring 2000 course that started
with
1. Probability Theory, 2. Financial Instruments, 3. Basic Principles of
Asset Evaluations, 4. One Period Asset Valuation, One Period Pricing
Model,
5. Discrete Time Model, Arbitrage and Martingales, Complete Markets,
6. American Options, Supermartingales and Snell Envelope, Stopping Time,
Decomposition of Supermartingales, 7. Continuous Time Model for Stock
Prices,
Brownian Motion, Continuous Martingale Stochastic Calculus, 8.
Black-Scholes
Differential Equation, The Market Price of Risk.
Comment: Section is CLOSED
Spring 2000 Courses
MISI Computational Financial Mathematics Track:
Fin 551 Financial Decision Making I, Spring 2000,
Prof. S. R. Pliska.
TIME: 21966 LECD 0415-0530 T R 0335 BSB
COURSE DESCRIPTION:
First foundation course for the study of modern financial economics. Two-period individual consumption and portfolio decisions under uncertainty and their implications for the valuation of securities
PREREQUISITES: Consent of the instructor.
This course is intended for both MBA students and grad
students from the math department. Besides an interest in finance,
students should be familiar with calculus, elementary probability theory,
and linear algebra. Some introductory knowledge of stochastic
processes and optimization theory, especially linear programming, would be
helpful but is not mandatory. It would not hurt to have had a
course or two in finance and/or economics.
TEXT: Introduction to Mathematical Finance: Discrete Time Models
by Stanley R. Pliska, Blackwell Publishers.
The class will cover most of this book.
Information about my book, including the Table of Contents, can be found on
my web page
http://www.uic.edu/~srpliska/IntroMF.html.
COMMENTS: Overview:
The aim is to learn some basic theory about financial markets,
especially the financial economic theory associated with
derivatives and portfolio management. Although this material will be
presented in a mathematically rigorous fashion, by studying discrete
time models of securities the level of math will be kept relatively
elementary. Nevertheless, we will be studying principles are of
fundamental importance, namely, principles that play important roles in the
modern financial industry. This course is intended for
students who like mathematical economics, quantitative subjects in finance
like futures and options, and financial engineering. It is ideal
for students who are intending to subsequently take more advanced courses in
the area of mathematical finance.
Math 590 Advances Topics in Applied Mathematics:
Financial Mathematics on Options Pricing, Spring 2000, Prof. S. S. T. Yau
TIME: 61916 LECD 1200-1250 M W F 0212 TH
PREREQUISITES:
Calculus
TEXT(S):
S. N. Neftci, An Introduction to the Mathematics of Financial Derivatives
, Academic Press.
COURSE DESCRIPTION:
1. Probability Theory, 2. Financial Instruments, 3. Basic Principles of
Asset Evaluations, 4. One Period Asset Valuation, One Period Pricing Model,
5. Discrete Time Model, Arbitrage and Martingales, Complete Markets,
6. American Options, Supermartingales and Snell Envelope, Stopping Time,
Decomposition of Supermartingales, 7. Continuous Time Model for Stock Prices,
Brownian Motion, Continuous Martingale Stochastic Calculus, 8. Black-Scholes
Differential Equation, The Market Price of Risk.
COMMENTS:
I shall keep the prerequisites as small as possible,
i.e., the course will be more of less self-contained. However, it is good
to have exposure in probability and differential equations.
Fall 1999 Courses
MISI Computational Financial Mathematics Track:
Math 590 Advances Topics in Applied Mathematics:
Financial Mathematics, Prof. C. Tier
Call/Time/Place: 65595 LECD 1200-1250 M W F 0307 AH
COURSE DESCRIPTION:
Finance is one of the fast growing areas in the
corporate world. Along with this, the explosion in financial instruments
has led ot the development of new mathematical models and methods
for their analysis. The course begins with a review of financial derivatives
and their applications. Models of financial derivatives will be presented
such as Black-Scholes model. The approach will be baseed on partial
differential equations using analytic and numerical methods.
PREREQUISITES:
Background in differential equations and
introductory probability or consent of the instructor.
TEXT(S):
Wilmot, Howison, and Dewynne, The Mathematics of Financial Dervatives;
A Student Introduction, Cambridge University Press.
Fin 551 Financial Decision Making, Stanley R. Pliska Description: This course will cover much of Professor
Pliska's book Introduction to Mathematical Finance, which as the name
suggests is a theoretical yet introductory study of security markets
including stocks, bonds, futures, and options. Considerable attention
will be. given to topics in financial economics such as arbitrage, risk
neutral valuation of derivative securities, and optimal
consumption/investment problems where the objective is to maximize
expected utility. Although the course will involve mathematics
presented in a rigorous fashion, the only mathematical prerequisites
are knowledge about probability, calculus, linear algebra, and
optimization, so economics students who have completed the first year
of graduate study should be well qualified. No particular courses in
finance are prerequisites, but students should come with an interest in
financial markets.
Math 586 Computational Finance, Charles Tier Description: The course begins with a review of financial
derivatives and their applications. Models of financial derivatives
will be presented such as Black-Scholes model. Models of exotic options
as well as interest rate products will be studied in depth. The
approach will be based on partial differential equations using analytic
and numerical methods.
Fin 571 Empirical Issues in Finance, Gilbert W. Bassett, Jr. Description: The course will cover empirical applications
focusing on financial equity data. The course will introduce robust
statistical methods, compare them to standard methods, and present
their application to problems in Finance. Problems to be considered
include the predictability of asset returns, analysis of market
microstructure, multifactor models for predicting returns, risk neutral
distributions implicit in options prices, and forecasting portfolio
tracking error.
Math 574 Applied Optimal Control. Floyd B. Hanson. Description:
Introduction to optimal control theory; calculus of variations, maximum
principle, dynamic programming, feedback control, linear systems with
quadratic criteria, singular control, optimal filtering, stochastic
control.
Math 584 Applied Stochastic Models. Charles Knessl. Description:
Applications of stochastic models in chemistry, physics, biology,
queueing, filtering, and stochastic control, diffusion approximations ,
Brownian motion, stochastic calculus, stochastically perturbed
dynamical systems, first passage times.
MCS 571 Numerical Methods for Partial Differential Equations. Floyd
B. Hanson. Description:
Finite difference methods for parabolic, elliptic, and hyperbolic
differential equations: explicit, Crank- Nicolson implicit, alternating
directions implicit, Jacobi, Gauss-Seidel, successive over-relaxation,
conjugate gradient, Lax-Wendroff, Fourier stability.
Math 480 Applied Partial Differential Equations. Various
Instructors. Description:
Initial value and boundary value problems for second order linear
equations, Eigenfunction expansions and Strum-Liouville theory, Green's
functions, Fourier transform,. Characteristics,. Laplace transform.
Math 590 Principles of Financial Mathematics, Stephen S. T. Yau Description: 1. Probability Theory, 2. Financial
Instruments, 3. Basic Principles of Asset Evaluations, 4. One Period
Asset Valuation, One Period Pricing Model, 5. Discrete Time Model,
Arbitrage and Martingales, Complete Markets, 6. American Options,
Supermartingales and Snell Envelope, Stopping Time, Decomposition of
Supermartingales, 7. Continuous Time Model for Stock Prices, Brownian
Motion, Continuous Martingale Stochastic Calculus, 8. Black-Scholes
Differential Equation, The Market Price of Risk.