A graduate course in the Mathematics in Finance program at the Courarant Institute of Mathematical Sciences of New York University.

**Instructor: **Professor Jonathan
Goodman,

**Meeting:** Warren Weaver Hall , room 101, Wednesday evenings 5
to 7 pm.

**First Class: **September 8, 1997

**Prerequisites: **Scientific
Computing, Mathematics
of Finance II. This these courses cover basic numerical analysis and
mathematical finance. If you have not taken the courses but think you have
the background for the course, contact the instructor.

**Grading: **The grade will be based on weekly assignments, mostly
computational.

**Course description**: Computational techniques for solving mathematical
problems arising in finance. Numerical solution of parabolic partial differential
equations, basic schemes, general theory, relation to binomial and trinomial
trees, boundary conditions for American options, computation of sensitivities,
application to one factor and multi factor models. Stochastic simulation
and Monte Carlo. Pseudo random number generators, generating random variables
with specified distributions, statistical analysis of simulation data and
error bars. Numerical solution of stochastic differential equations. Application
to pricing, hedging, and portfolio management. Path dependent options.
Model calibration and hypothesis testing. Value at risk.

**Lectures:**

Week 1: Dynamic programming, basic probability and Markov chains, forward and backward inductive computation of probabilities, expected values, and optimal decisions under uncertainty. The notes, in LaTeX format, Postscript format, or HTML, as of September 15. I will try to make the HTML a little better looking soon.

More materials will be posted when the course is going. In the mean time, you can look at materials from Fall 1995, or Fall 1996, or Fall 1997.

**Homework assignments**

Assignment 1, in postscript format, in LaTeX format, or in HTML (a last resort).

Assignment 2, in postscript format, in LaTeX format, or in HTML.

Assignment 3, in postscript format, in LaTeX format, and (soon) HTML format, along with the data file

Assignment 4, in postscript format, in LaTeX format.

Make sure to check the homework comments and hints page often while doing assignments.

**Lecture notes**

I will be updating the notes from last year and adding new ones as the term progresses. They will be posted here as they become available. Look through the old ones to see what's coming.

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