The optimal discretization of probability density functions

@article{citeulike:2735796, abstract = {The discretization of probability density functions (pdf's) is often necessary in financial modelling, especially in derivatives pricing and hedging, where certain pdf characteristics (e.g. fat tails) can have a disproportionate effect on prices. We present an exact dynamic programming (DP) algorithm to perform such a discretization optimally. We investigate the parallelisation of the DP algorithm and show that an almost linear speed-up is possible. For a large number of dimensions an approximate algorithm for the discretization of multivariate pdf's is presented. Computational results are reported for all variants of the algorithm when applied to different pdf's with various required levels of discretization.}, author = {Christofides, A. and Tanyi, B. and Christofides, S. and Whobrey, D. and Christofides, N.}, citeulike-article-id = {2735796}, doi = {10.1016/S0167-9473(99)00043-2}, journal = {Computational Statistics \& Data Analysis}, keywords = {density\_estimation, discretisation, dynamic\_programming, function\_approximation, probability}, month = {October}, number = {4}, pages = {475--486}, posted-at = {2008-04-30 01:42:46}, priority = {2}, title = {The optimal discretization of probability density functions}, url = {http://dx.doi.org/10.1016/S0167-9473(99)00043-2}, volume = {31}, year = {1999} }

TY - JOUR ID - citeulike:2735796 L3 - citeulike-article-id:2735796 N2 - The discretization of probability density functions (pdf's) is often necessary in financial modelling, especially in derivatives pricing and hedging, where certain pdf characteristics (e.g. fat tails) can have a disproportionate effect on prices. We present an exact dynamic programming (DP) algorithm to perform such a discretization optimally. We investigate the parallelisation of the DP algorithm and show that an almost linear speed-up is possible. For a large number of dimensions an approximate algorithm for the discretization of multivariate pdf's is presented. Computational results are reported for all variants of the algorithm when applied to different pdf's with various required levels of discretization. IS - 4 JF - Computational Statistics & Data Analysis EP - 486 TI - The optimal discretization of probability density functions VL - 31 SP - 475 KW - density_estimation KW - discretisation KW - dynamic_programming KW - function_approximation KW - probability AU - Christofides, A AU - Tanyi, B AU - Christofides, S AU - Whobrey, D AU - Christofides, N PY - 1999/10/28/ UR - http://dx.doi.org/10.1016/S0167-9473(99)00043-2 ER -