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Article Dans Une Revue Methodology and Computing in Applied Probability Année : 2023

How many inner simulations to compute conditional expectations with least-square Monte Carlo?

Résumé

The problem of computing the conditional expectation E[f (Y)|X] with least-square Monte-Carlo is of general importance and has been widely studied. To solve this problem, it is usually assumed that one has as many samples of Y as of X. However, when samples are generated by computer simulation and the conditional law of Y given X can be simulated, it may be relevant to sample K ∈ N values of Y for each sample of X. The present work determines the optimal value of K for a given computational budget, as well as a way to estimate it. The main take away message is that the computational gain can be all the more important that the computational cost of sampling Y given X is small with respect to the computational cost of sampling X. Numerical illustrations on the optimal choice of K and on the computational gain are given on different examples including one inspired by risk management.
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Dates et versions

hal-03770051 , version 1 (08-09-2022)
hal-03770051 , version 2 (11-05-2023)

Identifiants

Citer

Aurélien Alfonsi, Bernard Lapeyre, Jérôme Lelong. How many inner simulations to compute conditional expectations with least-square Monte Carlo?. Methodology and Computing in Applied Probability, 2023, 25 (3), pp.71. ⟨10.1007/s11009-023-10038-x⟩. ⟨hal-03770051v2⟩
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