In this paper we investigate some aspect of the partial realization problem formulated for Schur-functions considered on the right half plane of C. This analysis can be considered to be partially complementary to the results of A. Lindquist, C. Byrnes et al. on Carathéodory functions, , , . 1 Preliminaries and notation Let F be a rational p × m… (More)
We consider interest rate models where the forward rates are allowed to be driven by a multidimensional Wiener process as well as by a marked point process. Assuming a deterministic volatility structure, and using ideas from systems and control theory, we investigate when the input-output map generated by such a model can be realized by a finite dimensional… (More)
We present an approach for pricing of illiquid bonds (and bond derivatives) in an arbitrage-free way and consistently with observed prices of liquid bonds. The basic model is a multifactor term structure model with abstract latent factors. The approach is based on stochastic filtering techniques, leading to a continuous update of the distribution of the… (More)
We present an alternative approach to the pricing of bonds and bond derivatives in a multivariate factor model for the term structure of interest rates that is based on the solution of an optimal stochastic control problem. It can also be seen as an alternative to the classical approach of computing forward prices by forward measures and as such can be… (More)
We investigate here a parametrization of matrix Schur and positive real functions of degree n with given interpolating conditions. The results are presented for matrix valued functions.
We consider an affine term structure model of interest rates, where the factors satisfy a linear diffusion equation. We assume that the information available to an agent comes from observing the yields of a finite number of traded bonds and that this information is not sufficient to reconstruct exactly the factors. We derive a method to obtain… (More)
In this paper we investigate some aspect of the Nevanlinna-Pick and Schur interpolation problem formulated for Schur-functions considered on the right-half plane of C. We consider the well established parametrization of the solution Q = T Θ (S) := (SΘ 12 + Θ 22) −1 (SΘ 11 + Θ 21) (see e.g. ,), where the J-inner function Θ is completely determined by… (More)
The paper presents a study of several problems related to spectral factorizations. We assume only a very weak form of coercivity for the p × p spectral function Φ and look at the set W m of all rectangular, p × m spectral factors. The main object is the arithmetization of the geometry of the set of minimal, stable spectral factors by employing Hardy space… (More)
We present a new parametrization of inner functions based on the Schur algorithm. We make use of state space formulas (in practice we obtain a new parametrization of observable pairs). The main advantage of our parametrization is that for each chart the observability gramian is constant: this leads to a very good behavior in some approximation problems.