Assessing the probability of rare and extreme events is an important issue in the risk management of financial portfolios. Extreme value theory provides the solid fundamentals needed for the statistical modelling of such events and the computation of extreme risk measures. The focus of the paper is on the use of extreme value theory to compute tail risk measures and the related confidence intervals, applying it to several major stock market indices.
Climate change affects hydropower production by modifying total annual inflow volumes and their seasonal distribution. Moreover, increasing air temperatures impact electricity consumption and, as a consequence, electricity prices. All together, these phenomena may lead to a loss in revenue. We show that an adequate management of hydropower plants mitigates these losses. These results are obtained by resorting to an interdisciplinary approach integrating hydrology, economy and hydropower management in an interdependent quantitative model
Before introducing heuristic optimization methods and providing an overview of some applications in econometrics, we have to motivate the use of such an optimization paradigm in econometrics. Obviously, optimization is at the core of econometric applications to real datasets, e.g., in model selection and parameter estimation. Consequently, econometrics is a field with a long tradition in applying the most up-to-date optimization techniques.Maybe the most widely used technique is least squares estimation for linear models. The optimization problem in this case results in a system of linear equations that can be solved by standard techniques from linear algebra. However, in the case of ill-conditioned matrices, e.g., due to very high multicollinearity, or huge models, even this simple model might pose some numerical problems.A more demanding class of optimization problems stems from general maximum likelihood estimation. As long as the likelihood function can be considered as being globally convex, efficient numerical methods are available to solve the optimization problem. However, in this class of models, the number of notorious cases with flat
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.