Variance reduction has always been a central issue in Monte Carlo experiments. Population Monte Carlo
can be used to this effect, in that a mixture of importance functions, called a D-kernel, can be iteratively
optimized to achieve the minimum asymptotic variance for a function of interest among all possible mixtures.
The implementation of this iterative scheme is illustrated for the computation of the price of a European
option in the Cox-Ingersoll-Ross model. A Central Limit theorem as well as moderate deviations
are established for the D-kernel Population Monte Carlo methodology.