  This paper studies the multilevel Monte-Carlo estimator for the expectation
of a maximum of conditional expectations. This problem arises naturally when
considering many stress tests and appears in the calculation of the interest
rate module of the standard formula for the SCR. We obtain theoretical
convergence results that complements the recent work of Giles and Goda and
gives some additional tractability through a parameter that somehow describes
regularity properties around the maximum. We then apply the MLMC estimator to
the calculation of the SCR at future dates with the standard formula for an ALM
savings business on life insurance. We compare it with estimators obtained with
Least Square Monte-Carlo or Neural Networks. We find that the MLMC estimator is
computationally more efficient and has the main advantage to avoid regression
issues, which is particularly significant in the context of projection of a
balance sheet by an insurer due to the path dependency. Last, we discuss the
potentiality of this numerical method and analyze in particular the effect of
the portfolio allocation on the SCR at future~dates.
