Integration quadratures in discretization of stochastic programs

Because of its simplicity, conditional sampling is the most popular method for generating scenario trees in stochastic programming. It is based on approximating probability measures by empirical ones generated by random samples. Because of computational restrictions, these samples cannot be very large, so the empirical measures can be poor approximations of the original ones. This paper shows that modern integration quadratures provide a simple and an attractive alternative to random sampling. These quadratures are designed to give good approximations of given (probability) measures by a small number of quadrature points. The performance of the resulting scenario generation methods is demonstrated by numerical examples