In many (if not most) real-world applications, the arrival of customers to a service center is not well described by renewal processses. Quite often, the times between successive arrivals are correlated, whereas renewal processes have independent interarrival times. A natural generalization is the class of semiMarkov processes (SMP), which when specifically applied to the arrival of customers a...

We consider a semi-Markov modulated security market consisting of a riskless asset or bond with constant interest rate and risky asset or stock, whose dynamics follow gemoetric Brownian motion with volatility that depends on semi-Markov process. Two cases for semi-Markov volatilities are studied: local current and local semi-Markov volatilities. Using the martingale characterization of semi-Mar...