The 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 and so-called LIBOR rates, rather than on the instantaneous continuously compounded rates as in most traditional models. Forward and...

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 paper offers a new perspective on optimal portfolio choice by investigating how and to what extent knowledge of an investor's desirable initial investment choice can be used to determine his future optimal portfolio allocations. Optimality of investment decisions is built on the so-called...

This paper uses martingale calculus in order to study multiplicative Kac functionals. Probabilistic representation of a solution of the Schrodinger equation with non necessarily negative potential is obtained. Necessary and sufficient conditions for the a.s. convergence and the a.s. divergence...

A term structure model with lognormal type volatility structure is proposed. The Heath, Jarrow and Morton (HJM) framework, coupled with the theory of stochastic evolution equations in infinite dimensions, is used to show that the resulting rates are well defined (they do not explode) and remain...

A new dynamic criterion for measuring the performance of self-financing investment strategies is introduced. To this aim, a family of stochastic processes defined on [0, ∞) and indexed by a wealth argument is used. Optimality is associated with their martingale property along the optimal...

For a d-dimensional gaussian martingae M with tensor increasingprocess we prove that <M>+tMt converges in Rd with probability 1 as t --> [infinity] and the limit is zero a.s. iff tr <M>+t tends to zero. We apply this result to study the strong consistency of estimates in a linear regression model.

A semimartingale driven continuous time linear regression model is studied. Assumptions concerning errors allow us to consider also models with infinite variance. The order of the almost sure convergence of a class of estimates which includes least squares estimates is given. In the presence of...

Multiple linear regression models with non random regressors in continuous time are considered. The strong consistency of least squares estimates is established under minimal assumptions on the design when the process of errors is a semimartingale satisfying some regularity condition.

The problem of optimal linear estimation for continuous time processes is investigated. The signal and observation processes are solutions of a linear system. The optimal filter is given by recursive equations which reduce to the classical Kalman-Bucy equations when the system is driven by...