We review some recent advances in high-dimensional numerical integration, namely, in (i) optimal quantization of probability distributions, (ii) Quasi-Monte Carlo (QMC) methods, (iii) sparse grid methods. In particular, the methods (ii) and (iii) may be superior compared to Monte Carlo (MC) methods under certain conditions on the integrands. Some related open questions are also discussed. In the second part of the talk we present a model for optimizing electricity portfolios under demand and price uncertainty and argue that electricity companies are interested in risk-averse decisions. We explain how the stochastic data processes are modeled and how scenarios may be generated by QMC methods followed by a tree generation procedure. We present solutions for the risk-neutral and risk-averse situation, discuss the costs of risk aversion and provide several possibilities for risk aversion by multi-period risk measures.