Browsing by Author "Zhang, Lifeng"

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    The geometric Markov renewal processes with application to finance
    (2012) Zhang, Lifeng; Chen, Gemai; Swishchuk, Anatoliy
    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.