Bayesian Portfolio Optimization for Electricity Generation Planning
Nowadays, there are several electricity generation technologies based on the different sources, such as wind, biomass, gas, coal, and so on. Considering the uncertainties associated with the future costs of such technologies is crucial for planning purposes. In the literature, the allocation of resources in the available technologies have been solved as a mean-variance optimization problem using the expected costs and the correspondent covariance matrix. However, in practice, the expected values and the covariance matrix of interest are not exactly known parameters. Consequently, the optimal allocations obtained from the mean-variance optimization are not robust to possible errors in the estimation of such parameters. Additionally, there are specialists in the electricity generation technologies participating in the planning process and, obviously, the consideration of useful prior information based on their previous experience is of utmost importance. The Bayesian models consider not only the uncertainty in the parameters, but also the prior information from the specialists. In this paper, we introduce the Bayesian mean-variance optimization to solve the electricity generation planning problem using both improper and proper prior distributions for the parameters. In order to illustrate our approach, we present an application comparing the Bayesian with the naive mean-variance optimal portfolios.
KeywordsStatistics Inference methods Energy analysis Policy issues
The authors are grateful for the support of IME-USP, the Institute of Mathematics and Statistics of the University of São Paulo; FAPESP - the State of São Paulo Research Foundation (grants CEPID 2013/07375-0 and 2014/50279-4); and CNPq - the Brazilian National Counsel of Technological and Scientific Development (grant PQ301206/2011-2).
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