Tamed Euler interpolation multilevel Monte Carlo method for quadratic forward backward stochastic differential equations

We introduce a tamed Euler time-discretization method to approximate the analytical solutions of forward backward stochastic differential equations with generators of quadratic growth with respect to Z. Then we demonstrate that the time-discretization error of order of the tamed Euler scheme is 12 in the L2 sense. Moreover, a new estimator constructed based on the interpolation method and the multilevel Monte Carlo method is applied to approximate conditional expectations in the tamed Euler scheme. Compared with the interpolation Monte Carlo method, in our explicit tamed Euler scheme, this estimator reduces the computational complexity from O(ϵ−4−1r) to O(ϵ−2−1r), where ϵ denotes the prescribed accuracy and r represents the degree of polynomial interpolation functions. In a word, our proposed probabilistic numerical method has not only higher order but also lower computational complexity. Finally, numerical examples are given to illustrate our convergence results and significant computational savings.