Topic for a bachelor thesis: Multidimensional quadrature for computing expected values.

Description

Given a function depending on several random variables, the corresponding expected value is defined as a multidimensional integral. We can compute the integral approximately by a numerical quadrature. However, a multidimensional quadrature becomes critical in case of many random variables due to the curse of dimensionality. If the function is a multivariate polynomial, then the multidimensional integral results to a product of one-dimensional integrals. We consider a representation of the function by a linear combination using orthogonal basis polynomials. A numerical technique shall be constructed and implemented for the efficient computation of the multidimensional integrals. Thereby, predetermined values of one-dimensional integrals can be applied, which are computed for the basis polynomials a priori.

Required knowledge

• Introduction to Numerical Mathematics,
• Basics in Stochastics.

Literature

• J. Stoer, R. Bulirsch: Introduction to Numerical Analysis. Springer, Berlin, 2002. (for quadrature)