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Normal Deviation and Poisson Approximation of a Security Market by the Geometric Markov Renewal Processes |
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| Authors: | Anatoliy Swishchuk Md Shafiqul Islam |
| Affiliation: | 1. Department of Mathematics and Statistics , University of Calgary , Calgary , Alberta , Canada aswish@ucalgary.ca;3. Department of Mathematics and Statistics , University of Prince Edward Island , Charlottetown , Canada |
| Abstract: | We consider the geometric Markov renewal processes (GMRP) as a model for a security market. Normal deviations of the geometric Markov renewal processes for ergodic averaging and double averaging schemes are derived. We introduce Poisson averaging scheme for the geometric Markov renewal processes. European call option pricing formulas for GMRP are presented. |
| Keywords: | Diffusion approximation Double average of GMRP Ergodic average of GMRP European call options Geometric Markov renewal process (GMRP) Normal deviations Poisson approximation |