Cylindrical stochastic integration and applications to financial term structure modeling

We show that any given integral can be turned into a cylindrical integral by the simple application of a Hom functor. In this way, we construct a theory of cylindrical stochastic integration and cylindrical stochastic evolution equations. As an application in mathematical finance, we develop cylindrically measure-valued forward rate models. These can be used to describe term structures with jumps in the underlying at predictable times, as observed in interest rate and energy markets.