Geodesic
Minimum variance importance sampling via population Monte Carlo
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 427-447

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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.

DOI : 10.1051/ps:2007028
Classification : 60F05, 62L12, 65-04, 65C05, 65C40, 65C60
Keywords: adaptivity, Cox-Ingersoll-Ross model, Euler scheme, importance sampling, mathematical finance, mixtures, moderate deviations, population Monte Carlo, variance reduction 
@article{PS_2007__11__427_0,
     author = {Douc, R. and Guillin, A. and Marin, J.-M. and Robert, C. P.},
     title = {Minimum variance importance sampling via population {Monte} {Carlo}},
     journal = {ESAIM: Probability and Statistics},
     pages = {427--447},
     publisher = {EDP-Sciences},
     volume = {11},
     year = {2007},
     doi = {10.1051/ps:2007028},
     mrnumber = {2339302},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2007028/}
}
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Douc, R.; Guillin, A.; Marin, J.-M.; Robert, C. P. Minimum variance importance sampling via population Monte Carlo. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 427-447. doi: 10.1051/ps:2007028

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