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 -kernel Population Monte Carlo methodology.
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},
year = {2007},
publisher = {EDP Sciences},
volume = {11},
doi = {10.1051/ps:2007028},
mrnumber = {2339302},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps:2007028/}
}
TY - JOUR AU - Douc, R. AU - Guillin, A. AU - Marin, J.-M. AU - Robert, C. P. TI - Minimum variance importance sampling via population Monte Carlo JO - ESAIM: Probability and Statistics PY - 2007 SP - 427 EP - 447 VL - 11 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ps:2007028/ DO - 10.1051/ps:2007028 LA - en ID - PS_2007__11__427_0 ER -
%0 Journal Article %A Douc, R. %A Guillin, A. %A Marin, J.-M. %A Robert, C. P. %T Minimum variance importance sampling via population Monte Carlo %J ESAIM: Probability and Statistics %D 2007 %P 427-447 %V 11 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ps:2007028/ %R 10.1051/ps:2007028 %G en %F PS_2007__11__427_0
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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