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...

We consider the simultaneous linear minimax estimation problem in linear models with ellipsoidal constraints imposed on the unknown parameter. Using convex analysis we derive necessary and sufficient optimality conditions for a matrix to define the best linear minimax estimator. For certain...

In this paper, a simple Markov switching model for the volatility of financial returns is presented. We discuss a moment estimation procedure and develop forecasts for future squared volatilities.

In the framework of the classical Black and Scholes model of security market we present the explicit formulas of the minimal hedging portfolios for a number of reward processes of the ``classical'', lookback and Asian type. These results complement the solutions previously received by Mc~Kean,...

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...