Cylindrical stochastic integration and applications to financial term structure modeling

TL;DR

This paper introduces a new cylindrical solution concept for stochastic evolution equations, enabling advanced analysis of financial term structures with discontinuities, surpassing traditional solution limitations.

Contribution

It develops a novel cylindrical approach for stochastic equations that better models complex financial markets with discontinuities, addressing limitations of existing methods.

Findings

Cylindrical solutions effectively handle discontinuities in financial models.

The approach aligns well with the structure of large financial markets.

It overcomes key limitations of mild and weak solution frameworks.

Abstract

We develop a novel - cylindrical - solution concept for stochastic evolution equations. Our motivation is to establish a Heath-Jarrow-Morton framework capable of analysing financial term structures with discontinuities, overcoming deep stochastic-analytic limitations posed by mild or weak solution concepts. Our cylindrical approach, which we investigate in full generality, bypasses these difficulties and nicely mirrors the structure of a large financial market.