# Four vignettes from mathematical finance

### Dr. Richard Holmes

### HIM&R, Inc.

### Thursday, November 6, 1997, 4:00-5:00 PM

### Room 102, Bradley Hall

The relatively new discipline of "financial engineering" has
developed into an exciting area of applied probability and stocahstic analysis.
In this introductory talk I will discuss 4 problems from the world of finance
and investment, and show how some suitable mathematics can provide insight
into their solution. The problems, in increasing order of difficulty, are

1) If you have some extra disposable income, should you use it to pay
down your mortgage?

2) How should you do asset allocation?

3) Given a bunch of random variables, representing the uncertain future
returns of some assets (securities), what determines their current prices?

4) In particular, what if one of these assets depends on the price of
another? These are called "derivatives", and include stock options
as a special case.

The relevant mathematics will be a mix of calculus, linear algebra,
and probability.