Heath-Jarrow-Morton-Musiela equation with L\'evy perturbation
Micha{\l} Barski, Jerzy Zabczyk
TL;DR
This paper analyzes the Heath-Jarrow-Morton-Musiela equation with Lévy perturbations, establishing conditions for local and global existence of solutions in weighted function spaces, especially for linear diffusion cases.
Contribution
It provides new sufficient conditions for the existence of solutions to the HJM-Musiela equation with Lévy noise, advancing understanding of its mathematical properties.
Findings
Conditions for local and global existence are derived.
For linear diffusion, conditions are nearly necessary for global existence.
The analysis is conducted in weighted function spaces on [0,+∞).
Abstract
The paper studies the Heath-Jarrow-Morton-Musiela equation of the bond market. The equation is analyzed in weighted spaces of functions defined on . Sufficient conditions for local and global existence are obtained . For equation with the linear diffusion term the conditions for global existence are close to the necessary ones.
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