21st Annual Kenneth C. Schraut Memorial Lecture: "One Health: Connecting Humans, Animals and the Environment" (Suzanne Lenhart, University of Tennessee)

Plenary talk: "The Crossings of Art, History, and Mathematics" (Jennifer White, St. Vincent College)

]]>This research was supported by NSF grant NSF-DMS 0552577 and was conducted during an 8-week summer research experience for undergraduates (REU).

]]>Acknowledgements: We would like to thank our teacher Scott Mitter for all that he has done for us. From making waffles to teaching triple integrals, his input and encouragement have been invaluable. We would also like to thank the University of Dayton faculty for allowing us to participate in the UD Mathematics Day and to continue this paper.

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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- Scholes-Merton 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.

]]>A time scale, T, is a nonempty, closed subset of the real numbers, R. Several methods of solution exist for second order linear equations on a time scale. An advantage of these methods is that we can obtain solutions on a system comprising of continuous and/or discrete elements. After restricting the time scale to be R, these solutions are equivalent to those obtained using differential equations methods.

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