%% Papers Published
@article{fds296271,
Author = { Harrison Potter},
Title = {On Conformal Mappings and Vector Fields},
Journal = {OhioLINK Electronic Theses and Dissertations
Center},
Year = {2008},
Month = {May},
url = {http://etd.ohiolink.edu/view.cgi?acc_num=marhonors1210888378},
Abstract = {We seek to extend the applicability of the tools of complex
analysis that have been developed to deal with problems in
twodimensional harmonic field theory. In order to ease the
reader who has only a basic understanding of complex
analysis into a working knowledge of its relevant
applications to field theory, this material is introduced
through the use of vector fields as common ground.
Opportunities for using the mathematical tools being
developed to solve physical problems are also highlighted by
examples in order to aid comprehension and foster intuition.
Established techniques used in solving problems involving
point sources are then generalized to handle those involving
interval sources.},
Key = {fds296271}
}
@article{fds296272,
Author = {VX Dang and H Potter and S Glasgow and S Taylor},
Title = {Pricing the Asian Call Option},
Journal = {Electronic Proceedings of Undergraduate Mathematics
Day},
Volume = {3},
Number = {3},
Pages = {26},
Year = {2008},
Month = {February},
url = {http://academic.udayton.edu/EPUMD/},
Abstract = {Background material on measuretheoretic probability theory
and stochastic calculus is provided in order to clarify
notation and inform the reader unfamiliar with these
concepts. These fields are then employed in exploring two
distinct but related approaches to fair option pricing:
developing a partial differential equation whose solution,
given specified boundary conditions, is the desired fair
option price and evaluating a riskneutral conditional
expectation whose value is the fair option price. Both
approaches are illustrated by example before being applied
to the Asian call option. Two results are obtained by
applying the latter option pricing approach to the Asian
call option. The price of an Asian call option is shown to
be equal to an integral of an unknown joint distribution
function. This exact formula is then made approximate by
allowing one of the random variables to become a parameter
of the system. This modified Asian call option is then
priced explicitly, leading to a formula that is strikingly
similar to the Black ScholesMerton formula, which prices
the European call option. Finally, possible methods of
generalizing the procedure to price the Asian call option
both exactly and explicitly are speculated.},
Key = {fds296272}
}
