Diffusion approximations of the geometric Markov ...

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Title Diffusion approximations of the geometric Markov renewal processes and option price formulas
Author(s) S. Anatoliy, Shafiqul Islam
Journal International Journal of Stochastic Analysis
Date 2010
Volume 2010
Issue
Abstract We consider the geometric Markov renewal processes as a model for a security
market and study this processes in a diffusion approximation scheme. Weak convergence
analysis and rates of convergence of ergodic geometric Markov renewal processes in diffusion
scheme are presented. We present European call option pricing formulas in the case of
ergodic, double-averaged, and merged diffusion geometric Markov renewal processes.

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