A NON-INTRUSIVE STRATIFIED RESAMPLER FOR REGRESSION MONTE CARLO: APPLICATION TO SOLVING NON-LINEAR EQUATIONS

Our goal is to solve certain dynamic programming equations associated to a given 5 Markov chain X, using a regression-based Monte Carlo algorithm. More specifically, we assume that 6 the model for X is not known in full detail and only a root sample X1, . . . , XM of such process 7 is available. By a stratification of the space and a suitable choice of a probability measure ν, we 8 design a new resampling scheme that allows to compute local regressions (on basis functions) in each 9 stratum. The combination of the stratification and the resampling allows to compute the solution to 10 the dynamic programming equation (possibly in large dimensions) using only a relatively small set 11 of root paths. To assess the accuracy of the algorithm, we establish non-asymptotic error estimates 12 in L2(ν). Our numerical experiments illustrate the good performance, even with M = 20 − 40 root 13 paths. 14

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