MOMENTS OF 2ND-ORDER POLYNOMIALS WITH SIMULATION APPLICATIONS

Practical solutions to complicated sampling problems can often be found through the use of polynomial approximators. The approximators can yield exact expressions for (approximate) statistical properties, such as moments, obviating the need for sampling; on the other hand, should sampling be used, the approximators can be applied as control variates to sharpen Monte Carlo results. In this paper we give exact expressions for the first three moments of second order polynomials of independent and identically distributed random variables. The utility of these polynomials is illustrated in three examples: The first concerns the evaluation of the moments of the sample variance, the second investigates properties of a present value when interest rates vary, and the third involves control variates in a complicated sampling problem with nonlinear regression. © 1990 Taylor & Francis Group, LLC.