Time Scales in Economics and Finance

Missouri University Of Science And Technology, Rolla MO

Investigators

Abstract

In this project, the principal investigator seeks to expand his research program in Applied Mathematics into Economics and Finance. The PI will spend the 2007-2008 academic year in the Economics and Finance Department at his home institution, University of Missouri-Rolla. The purpose of this visit is to establish an independent research program focused on applications of the theory of dynamic equations on time scales (including difference and differential equations) in various areas of economics and finance, to develop fruitful collaboration with economists, and to establish an interdisciplinary master's degree course in Financial Mathematics. The PI will collaborate with Professor Gelles, Chair of the Economics and Finance Department, as well as with other members of that department and with economists and applied mathematicians working in finance worldwide in order to apply the recently developed and exciting theory of time scales (which allows to unify the continuous and the discrete and to extend those to other in between cases) to develop among others unification and extension theories for the following concepts: (i) stochastic differential equations and stochastic difference equations, (ii) continuous-time financial market models and discrete-time financial market models, (iii) continuous interest rate theory and discrete interest rate theory. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).