The point estimator used in naive Monte Carlo sampling weights all the computed function evaluations equally, and it does not take into account the precise locations at which the function evaluations are made. In this note, we consider one-dimensional integration problems in which the integrand...

We show that in the world of Black and Scholes (1973) lookback options where the underlying price is monitored discretely instead of continuously can be priced in semi-closed form. We derive pricing formulas for a variety of full and partial lookback options, where monitoring takes place at not...

An explicit finite difference scheme for the numerical solution of the diffusion equation on a rectangular region, subject to a non-local boundary condition in the form of a double integral which simulates the specificaion of mass in a curved region is developed. The scheme, is based on the...