• Corpus ID: 252780984

Cylindrical stochastic integration and applications to financial term structure modeling

@inproceedings{Assefa2022CylindricalSI,
  title={Cylindrical stochastic integration and applications to financial term structure modeling},
  author={Johannes Assefa and Philipp Harms},
  year={2022}
}
. 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. 

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References

SHOWING 1-10 OF 38 REFERENCES

Cylindrical continuous martingales and stochastic integration in infinite dimensions

In this paper we define a new type of quadratic variation for cylindrical continuous local martingales on an infinite dimensional spaces. It is shown that a large class of cylindrical continuous

Term structure modelling for multiple curves with stochastic discontinuities

This work develops a tractable class of models, based on affine semimartingales, going beyond the requirement of stochastic continuity, and provides a fundamental theorem of asset pricing based on NAFLVR.

A weak stochastic integral in Banach space with application to a linear stochastic differential equation

Cylindrical Wiener processes in real separable Banach spaces are defined, and an approximation theorem involving scalar Wiener processes is given for such processes. A weak stochastic integral for

Measure-valued affine and polynomial diffusions

It is shown the so-called moment formula, i.e. a representation of the conditional marginal moments via a system of finite dimensional linear PDEs, and characterize the corresponding infinitesimal generators and obtain a representation analogous to polynomial diffusions on R+, in cases where their domain is large enough.

Stochastic Analysis on Nuclear Spaces and its Applications

This paper reviews the recent developments in the theory of stochastic processes with values in the nuclear spaces and gives an overview of the subject in such a way that the reader can use these results as soon as he becomes familiar with the concepts illustrated here.

Brownian Representations of Cylindrical Local Martingales, Martingale Problem and Strong Markov Property of Weak Solutions of SPDEs in Banach Spaces

The paper deals with three issues. First we show a sufficient condition for a cylindrical local martingale to be a stochastic integral with respect to a cylindrical Wiener process. Secondly, we state

Continuous local martingales and stochastic integration in UMD Banach spaces

Recently, van Neerven, Weis and the author, constructed a theory for stochastic integration of UMD Banach space valued processes. Here the authors use a (cylindrical) Brownian motion as an

Infinite-dimensional polynomial processes

We introduce polynomial processes taking values in an arbitrary Banach space B ${B}$ via their infinitesimal generator L $L$ and the associated martingale problem. We obtain two representations of

Isomorphism for Spaces of Predictable Processes and an Extension of the Ito Integral

The goal of this article is to give an easy proof that spaces of predictable processes with values in a Banach space are isomorphic to spaces of progressive resp. adapted, measurable processes. This