Fredrik Hellman: A multilevel Monte Carlo method for failure probabilities

We analyze the multilevel Monte Carlo method for the irregular failure probability functional (in some contexts known as the binary option functional). The failure probability is the value of the cumulative distribution function at a given threshold value for the random variable under consideration. We prove a sharp convergence rate for the MLMC corrector variance in the infinity norm of the approximation error and present a refinement strategy that makes the cost of the method asymptotically (with respect to sample size) proportional to solving the model problem for a single realization.