A new implementation for the one-dimensional Hull&White model is developed. It is motivated by a geometrical approach to construct an invariant manifold for the future dynamics of forward zero coupon bond prices under a forward martingale measure. This reduces the option-pricing problem for...

This paper presents a unified framework of different algorithms to numerically compute high order expansions of invariant manifolds associated to a steady state of a dynamical system. The framework is inspired in the parameterization method of Cabr, Fontich and de la Llave [7], and the...

We examine the existence of an invariant manifold in the phase space structure presented by a dissipative four-wave coupling. We show that, once in such manifold, the system preserves two quantities as time evolves: a quantity related to the energy of the system and another, related to the...

This paper discusses the inhomogeneous nonlinear Schrödinger equation with critical exponent. By constructing a variational problem and the so-called invariant manifolds of the evolution flow, we derive a sharp criterion for blowup and global existence of the solutions.

Invariant manifolds play an important role in the study of Dynamical Systems, since they help to reduce the essential dynamics to lower dimensional objects. In that way, a bifurcation analysis can easily be performed. In the classical approach, the reduction to invariant manifolds requires...

The purpose of this essay is to give an overview of some recent workconcerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. 1. When is a given forward rate model consistent with a given family...

The purpose of this essay is to give an overview of some recent workconcerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. <p> <p> 1. When is a given forward rate model consistent with a given...</p></p>