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
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.