Let M(X) be a family of all equivalent local martingale measures for some locally bounded d-dimensional process X, and V be a positive process. Main result of the paper (Theorem 2.1) states that the process V is a supermartingale whatever Q in M(X), if and only if this process admits the...

The rational expectations hypothesis is supported if rational expectations are stable with respect to reasonable learning procedures. We consider the Stochastic Gradient-Algorithm as a boundedly rational learning procedure in an univariate ARX-Model with forecast feedback. We prove that whenever...

In this study we consider a linear model with forecast feedback in which boundedly rational agents are learning the parameter values of the rational expectations equilibrium by the OLS learning procedure. We show strong consistency of the OLS estimates under much weaker assumptions on the...

In this paper it is shown that the space of stochastic integrals w.r. to a special semimartingal is closed and hence every square integrable random variable admits a best approximation in this space. In terms of financial economics this means that for every contingent claim there exists a...

pagehe problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices or LIBOR rates, rather than on the instantaneous rates as in the traditional models. Forward and spot probability measures are...

The purpose of this paper is to present a numerical method to solve partial stochastic differential equations. This concept remains the differential operator unchanged but discretizes the dimension of the problem. The response function will be decomposed by the Karhunen--Loeve expansion and...

If calibrated to an observed term structure of interest rates that only covers a finite range of times-to-maturity an HJM-model of the term structure of interest rates will eventually die out in finite time as bonds reach maturity. This poses problems for the pricing and hedging of certain...