Cylindrical stochastic integration

Abstract

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. Contents 1. Introduction 1 2. Cylindrical vector integration 2 3. Cylindrical stochastic analysis 6 4. Cylindrically measure-valued term structure models 8 Appendix A. Measurable and predictable versions 15 References 16