Anatoliy Pogorui & Anatoliy Swishchuk 
Random Motions in Markov and Semi-Markov Random Environments 2 
High-dimensional Random Motions and Financial Applications

This book is the second of two volumes on random motions in Markov
and semi-Markov random environments. This second volume focuses
on high-dimensional random motions.
This volume consists of two parts. The first expands many of the results
found in Volume 1 to higher dimensions. It presents new results on the
random motion of the realistic three-dimensional case, which has so far
been barely mentioned in the literature, and deals with the interaction of
particles in Markov and semi-Markov media, which has, in contrast,
been a topic of intense study.

The second part contains applications of Markov and semi-Markov
motions in mathematical finance. It includes applications of telegraph
processes in modeling stock price dynamics and investigates the pricing
of variance, volatility, covariance and correlation swaps with Markov
volatility and the same pricing swaps with semi-Markov volatilities.

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Anatoliy Pogorui?s main research interests include probability,
stochastic processes, mathematical modeling of an ideal gas using
multi-dimensional random motions and the interaction of telegraph
particles in semi-Markov environments and the application of random
evolutions in the reliability theory of storage systems.

Anatoliy Swishchuk is Professor of mathematical finance at the
University of Calgary, Canada. His research areas include financial
mathematics, random evolutions and their applications, stochastic
calculus and biomathematics.

Ramon M. Rodriguez-Dagnino has investigated applied probability
aimed at modeling systems with stochastic behavior, random motions in
wireless networks, video trace modeling and prediction, information
source characterization, performance analysis of networks with heavytail traffic, generalized Gaussian estimation and spectral analysis.