### Abstracts

** ****Eliezer Z. Prisman**, Schulich School
of Business, York University

*Arbitrage Violations and Implied Valuations: The Option Market*

A relatively recent trend in the option pricing literature is to impute
the Risk-Neutral {RN) distribution from market data rather than assuming
the distribution of the price of the underlying asset. Given the market
prices of European options, one solves for a RN distribution by satisfying
the pricing relation. Observed option prices are typically not free
of noise and thus usually do not represent arbitrage-free prices. Conducting
a study on the imputed RN distribution thus requires eliminating the
noise from the prices so they will represent arbitrage-free prices.

Not much attention, however, has been devoted to the process of cleaning
the data and no systematic, all-encompassing method has been developed
and employed. Methods used in previous literature verify the satisfaction
of necessary but not sufficient conditions for the data to be free of
arbitrage. This paper develops a necessary and sufficient condition
for the satisfaction of the No-Arbitrage {NA) condition in option markets.
A consequence of this condition renders the practice of solving for
the RN distribution based on discretization as being flawed and allows
for arbitrage even though a RN distribution exists for the discretization.
The paper also develops a simple and robust methodology that eliminates
all displayed arbitrage in option prices. A new procedure of RN distribution
estimation is suggested, based on the approximation of convex functions
that, until now, have not been utilized for this purpose. (joint work
with Ioulia D. Ioffe Carlson School of Management, University of Minnesota)

**Ulrich Haussmann**, University of British
Columbia

*Optimizing terminal wealth under partial observation (with J. Sass,
RICAM, Linz, Austria)*

Typically an investor does not know the instantaneous rates of return
of the stocks he holds; he only sees the stock prices. In the literature
these rates are frequently modeled as Gaussian processes so that Kalman
filtering can be applied to estimate them. We propose an alternate model,
a continuous time Markov chain with finitely many states possibly representing
the states of the economy. Filtering results are available and allow
us to give the optimal trading strategy for the problem of maximizing
the expected utility of terminal wealth. Parameters can be estimated
using the EM algorithm and the optimal strategy can be determined numerically
in some cases.

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