Suchergebnisse

Solid particle grinding is considered as a Markov process. Mathematical models of disintegration kinetics are classified on the basis of the class of Markov process that they belong to. A mathematical description of the disintegration kinetics of polydisperse particles by milling in a shock-loading grinder is proposed on the basis of the theory of Markov processes taking into account the operational conditions in the device. The proposed stochastic model calculates the particle size distribution of the material at any instant in any place in the grinder. The experimental data is in accordance with the predicted values according to the proposed model.

We propose a market–based approach to the modelling of implied volatility, in which the implied volatility surface is directly used as the state variable to describe the joint evolution of market prices of options and their underlying asset. We model the evolution of an implied volatility surface by representing it as a randomly fluctuating surface driven by a finite number of orthogonal random factors. Our approach is based on a Karhunen–Loeve decomposition of the daily variations of implied volatilities obtained from market data on SP500 and DAX options.We illustrate how this approach extends and improves the accuracy of the well–known 'sticky moneyness' rule used by option traders for updating implied volatilities. Our approach gives a justification for the use of 'Vegas' for measuring volatility risk and provides a decomposition of volatility risk as a sum of independent contributions from empirically identifiable factors.(J.E.L.: G130, C14, C31).