Local well-posedness of Musiela's SPDE with L\'evy noise

TL;DR

This paper establishes conditions under which Musiela's SPDE driven by Lévy noise has a unique local mild solution in weighted function spaces, advancing understanding of stochastic financial models.

Contribution

It provides new sufficient conditions for the existence and uniqueness of solutions to Musiela's SPDE with Lévy noise, extending previous results to more general noise types.

Findings

Identified conditions ensuring local well-posedness of Musiela's SPDE with Lévy noise

Proved existence and uniqueness of solutions in weighted function spaces

Extended classical results to include Lévy-driven stochastic models

Abstract

We determine sufficient conditions on the volatility coefficient of Musiela's stochastic partial differential equation driven by an infinite dimensional L{\'e}vy process so that it admits a unique local mild solution in spaces of functions whose first derivative is square integrable with respect to a weight.