Financial engineering is the application of mathematical models in the research, development and pricing of new financial instruments and services. Although the origins of financial engineering can be traced to the work of Bachelier in the early part of this century, a major breakthrough in the field was made in 1973 with the discovery of the option pricing formula.

It is often said that the option pricing formula is to financial economics what the double helix was to molecular biology. In biology, the discovery of the structure of DNA gave birth to a new field of immense practical importance -- genetic engineering. Similarly, the discovery of the option pricing formula gave birth to the equally important field of financial engineering.

Dr. Mack will discuss some applications of options analysis to risk management and investments analysis. Mathematical models in options analysis consist of a system of stochastic parabolic partial differential equations with fixed and/or moving boundary conditions. Dr. Mack will describe various known analytical solutions, as well as numerical approximations to the solution to these stochastic partial differential equations. Some industrial applications will also be described.

1996-1997 Mathematics in High Performance Computing