Steven
Shreve's Ph.D. is in mathematics from the University of Illinois,
and I also
hold an M.S. degree in electrical engineering and a B.A. degree in German.
My research has centered around stochastic control, and in 1980 I
began work
with John Lehoczky on extensions of the Merton capital asset
pricing model,
which is really a problem in stochastic control. Since that time,
I have worked
on the effect of transaction costs and uncertain volatility in the
Black-Scholes
model and the pricing and hedging of exotic options. More recently, I have
become interested in credit derivatives and credit risk. In 1991 I founded
the Ph.D. program in Mathematical Finance at Carnegie Mellon, and
was a member
of the committee which founded the Master's degree program in
Computational
Finance in 1994. My role in the Master's program is teaching
courses on stochastic
calculus methods which underly the models for equity and interest
rate derivatives.
I also teach two-day courses for RISK on stochastic calculus
models for finance.
With Ioannis Karatzas, I have coauthored the books "Brownian
Motion and Stochastic
Calculus" and "Methods of Mathematical Finance."
