  We briefly review our recent studies on stochastic processes modelling
internet on-line trading. We present a way to evaluate the average waiting time
between the observation of the price in financial markets and the next price
change, especially in an on-line foreign exchange trading service for
individual customers via the internet. The basic method of our approach depends
on the so-called renewal-reward theorem. Assuming that the stochastic process
modelling the price change is a renewal process, we use the theorem to
calculate the average waiting time of the process. The so-called ``inspection
paradox'' is discussed, which, in general, means that the average durations is
shorter than the average waiting time.
