### DIMACS Workshop on New Market Models

#### April 26 - 27, 1999

DIMACS Center, CoRE Building Auditorium, Rutgers University, Piscataway, NJ

#### Principal Organizers:

** Larry Shepp**, Rutgers University, shepp@stat.rutgers.edu
** Chris Heyde**, CAP, Columbia University, chris@wald.stat.columbia.edu

In the aftermath of the failure of Long Term Capital Management, it is
timely to reevaluate the standard modeling paradigms. In particular, it
must be questioned whether the Black-Scholes-Merton model for pricing of an
option on a particular stock is accurate enough. This model makes the
debatable assumption that arbitrage is impossible and that information is
shared equally by everyone in the market. The main hypothesis underlying
the theory is that there is complete information and that it never happens
that one can simultaneously buy and sell a stock or asset without risking
any money and secure a guaranteed profit. This gives rise to the celebrated
exponential Brownian motion model for stock market fluctuations, to the
theorem of existence of a self-financing portfolio of stocks and bonds whose
income stream is martingale, and to riskless investing.
New models for stock price fluctuations will be presented. For example, we
will consider a model in which, at certain times, insider information
influences the price and changes the fair price of the standard hedge
options. In this new model, the stock price is not a martingale, but fair
prices of the standard hedges can still be obtained.
This workshop will also address such topics/questions as:
- Are the hypotheses a valid basis for building a theory of the market, or
are they just a first approximation to the physical situation of marketing?
- Is the negation of the above hypothesis a more valid basis for axiomatics?
For example, is it reasonable to assume that there is always "arbitrage" and
always non-uniformity of available information about the state of the market.
- Other possible topics of discussion include, but are not limited to,
mathematical finance, in particular as it relates to topics that are
discrete in flavor. For example, we might consider implementation of
algorithms for option pricing calculations.

The goal of the workshop is to produce lively and productive debate on these
issues. After a tutorial presentation of the BS model, a panel of experts
will discuss the pros and cons of various models. The remainder of the
meeting will consist of individual invited papers, with a focus on new
methods and models.
PROGRAM COMMITTEE: Sid Browne, Goldman-Sachs; Darrell Duffie, Stanford
University; Xin Guo, Dan Ocone, Ted Petrie and Andrew Prekopa, Rutgers
University.

We anticipate a limited amount of funds available to support participants.

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Document last modified on February 26, 1999.