Heath-Jarrow-Morton-Musiela equation with L\'evy perturbation

The paper studies the Heath-Jarrow-Morton-Musiela equation of the bond market. The equation is analyzed in weighted spaces of functions defined on $[0,+\mathrm{\infty })$. 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.