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Minimum variance importance sampling via population Monte Carlo. (English) Zbl 1181.60028

Summary: 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.

MSC:

60F05 Central limit and other weak theorems
62L12 Sequential estimation
65-04 Software, source code, etc. for problems pertaining to numerical analysis
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
65C60 Computational problems in statistics (MSC2010)
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