Efficient Simulation for Expectations over the Union of Half-Spaces

Abstract

We consider the problem of estimating expectations over the union of half-spaces. Such a problem arises in many applications such as option pricing and stochastic activity networks. More recent applications include systemic risk measurements of financial networks. Assuming that random variables follow a multivariate elliptical distribution, we develop a conditional Monte Carlo method and prove its asymptotic efficiencies. We then demonstrate the numerical performance of the proposed method in three different application areas.