Multilevel nested simulation for efficient risk estimation

Michael B. Giles, Abdul-Lateef Haji-Ali

We investigate the problem of computing a nested expectation of the form $\mathbb{P}[\mathbb{E}[X|Y]\ge 0]=\mathbb{E}[\text{H}(\mathbb{E}[X|Y])]$ where $\text{H}$ is t…