In this paper we study a particular class of forward rate problems, related to the Vasicekmodel, where the driving equation is a linear Gaussian stochastic partial differentialequation. We first give an existence and uniqueness results of the related mild solutionin infinite dimensional setting, then we study the related Ornstein–Uhlenbeck semigroupwith respect to the determination of a unique invariant measure for the associated Heath–Jarrow–Morton–Musiela model.
Invariant measure for the Vasicek interest rate model in the Heath-Jarrow-Morton-Musiela framework
DI PERSIO, Luca
;CORDONI, Francesco Giuseppe
2015-01-01
Abstract
In this paper we study a particular class of forward rate problems, related to the Vasicekmodel, where the driving equation is a linear Gaussian stochastic partial differentialequation. We first give an existence and uniqueness results of the related mild solutionin infinite dimensional setting, then we study the related Ornstein–Uhlenbeck semigroupwith respect to the determination of a unique invariant measure for the associated Heath–Jarrow–Morton–Musiela model.
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