Weak error for nested Multilevel Monte Carlo

Daphné Giorgi (1) , Vincent Lemaire (1) , Gilles Pagès (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

This article discusses MLMC estimators with and without weights, applied to nested expectations of the form E [f (E [F (Y, Z)|Y ])]. More precisely, we are interested on the assumptions needed to comply with the MLMC framework, depending on whether the payoff function f is smooth or not. A new result to our knowledge is given when f is not smooth in the development of the weak error at an order higher than 1, which is needed for a successful use of MLMC estimators with weights.

Mots clés: Multilevel Monte Carlo; Weighted Multilevel Monte Carlo; Nested Monte Carlo; Weak error expansion

Domaines: Probabilités [math.PR]

Daphné Giorgi, Vincent Lemaire, Gilles Pagès. Weak error for nested Multilevel Monte Carlo. Methodology and Computing in Applied Probability, 2020, 22 (3), pp.1325-1348. ⟨10.1007/s11009-019-09751-3⟩. ⟨hal-01817386⟩