S. Herzel (University of Perugia)

Title:
Optimization Problems in Pricing and Hedging Options
Abstract:
The purpose of this tutorial is to illustrate the most
important concepts of the arbitrage pricing theory to an audience
whose expertise is mostly focused in the field of optimization. The
fundamental results on hedging and pricing of contingent claims will
be derived through the use of basic tools of duality theory. An
overview of the most significant applications of optimization's
techniques to some option pricing problems will also be given.
Presentation for download.

R. H. Tütüncü (Carnegie Mellon University)

Title:
Robust Optimization in Finance
Abstract:
Many optimization problems are formulated using parameters
whose true values are not known with certainty. Robust optimization
refers to a modeling strategy for such problems that intends to
obtain a solution that is guaranteed to perform adequately for all
or most possible realizations of these uncertain parameters. During
the last decade, an intensive study of robust formulations for many
classes of optimization problems using various uncertainty
structures have led to many successful algorithms and applications.
We will review some of these results and pay special attention to
current debates on the different interpretations of robustness such
as robustness in constraints vs. objective function, absolute vs.
relative robustness, adjustable robustness, etc. .
Optimization formulations of problems from financial mathematics
often involve parameters such as returns, interest rates, and
volatilities whose values will be realized in the future and
therefore are uncertain. Or, these parameters may represent
statistical quantities (means, covariances, etc.) associated with
random events whose true distributions are unobservable. Robust
optimization provides an ideal setting for addressing such
uncertainties in a conservative fashion. We will review some recent
applications of robust optimization approach to portfolio selection,
risk management, as well as pricing and hedging of derivative
securities.
Presentation for download:
part 1
and
part 2.

