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.
Part 1. Higher-dimensional Random Motions and Interactive Particles
1. Random Motions inHigher Dimensions.
2. System of Interactive Particles with Markov and Semi-Markov Switching.
Part 2. Financial Applications
3. Asymptotic Estimation for Application of the Telegraph Process as an Alternative to the Diffusion Process in the Black–Scholes Formula.
4. Variance, Volatility, Covariance and Correlation Swaps for Financial Markets with Markov-modulated Volatilities.
5. Modeling and Pricing of Variance, Volatility, Covariance and Correlation Swaps for Financial Markets with Semi-Markov Volatilities.
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.
Ramón M. Rodríguez-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 heavy-tail traffic, generalized Gaussian estimation and spectral analysis.
Table of Contents
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