In financial markets traders often protect their position from a significant decline by using a trailing stop. Assume the trader is long the market (owns the security). A trailing stop is an order to sell the security at the market, if the price of the security drops to the stop price. The stop...

Importance sampling is one of the classical variance reduction techniques for increasing the efficiency of Monte Carlo algorithms for estimating integrals. The basic idea is to replace the original random mechanism in the simulation by a new one and at the same time modify the function being...

The principal problem associated with steady-state simulation is the estimation of the variance term in an associated central limit theorem. This paper develops several strongly consistent estimates for this term using the strong approximations available for Brownian motion. A comparison of...