We study the dependence of mild solutions to linear stochastic evolution equations on Hilbert space driven by Wiener noise, with drift having linear part of the type A+εG, on the parameter ε. In particular, we study the limit and the asymptotic expansions in powers of ε of these solutions, as well as of functionals thereof, as ε→0, with good control on the remainder. These convergence and series expansion results are then applied to a parabolic perturbation of the Musiela SPDE of mathematical finance modeling the dynamics of forward rates.

Singular perturbations and asymptotic expansions for SPDEs with an application to term structure models

Albeverio, Sergio;Mastrogiacomo, Elisa
2023-01-01

Abstract

We study the dependence of mild solutions to linear stochastic evolution equations on Hilbert space driven by Wiener noise, with drift having linear part of the type A+εG, on the parameter ε. In particular, we study the limit and the asymptotic expansions in powers of ε of these solutions, as well as of functionals thereof, as ε→0, with good control on the remainder. These convergence and series expansion results are then applied to a parabolic perturbation of the Musiela SPDE of mathematical finance modeling the dynamics of forward rates.
2023
2022
Singular perturbations; Asymptotic expansions; Stochastic PDE; Interest rate models
Albeverio, Sergio; Marinelli, Carlo; Mastrogiacomo, Elisa
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2144651
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