Diffusion Approximations of the Geometric Markov Renewal Processes and Option Price Formulas

[摘要] We consider the geometric Markov renewal processes as a model for a securitymarket and study this processes in a diffusion approximation scheme. Weak convergenceanalysis and rates of convergence of ergodic geometric Markov renewal processes in diffusionscheme are presented. We present European call option pricing formulas in the case ofergodic, double-averaged, and merged diffusion geometric Markov renewal processes.

[学科分类] 应用数学