The geometric Markov renewal processes with application to finance
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2012
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Abstract
First, we give some basic concepts and properties on Markov and Semi-Markov Processes and Chains, along with Wiener process and Levy process, all of which are prepared for the next Generalized Geometric Markov Renewal Processes. Next,we introduce CoxRoss-Robinstein binomial model and Aase model, and based on them, generalized Geometric Markov Renewal Process models. Then, we consider geometric Markov renewal processes as models for a security market and also study the processes in a diffusion approximation and normal deviation scheme. As an application, we consider the case of two ergodic classes. We present European call option pricing formulas in the case of ergodic, double-averaged, and merged diffusion geometric markov renewal processes. Finally, we introduce Poisson averaging scheme for the geometric Markov renewal processes to obtain compound Poisson process with deterministic drift and derive its option price under risk-neutral measure. European call option pricing formulas for GMRP are presented. Key Words: Markov chains; Geometric markov renewal processes; Merged Markov space; Phase averaging; Double averaging; Diffusion approximations; European option pricing; Normal deviations; Poisson approximation.
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Bibliography: p. 107-109
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Citation
Zhang, L. (2012). The geometric Markov renewal processes with application to finance (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/4703