A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.Solvency II, Solvency Capital Requirement, Standard Model, Internal Model, Monte Carlo simulation, Copulas.

kk-means clustering of extremes

The $k$-means clustering algorithm and its variant, the spherical $k$-means clustering, are among the most important and popular methods in unsupervised learning and pattern detection. In this paper, we explore how the spherical $k$-means algorithm can be applied in the analysis of only the extremal observations from a data set. By making use of multivariate extreme value analysis we show how it can be adopted to find "prototypes" of extremal dependence and we derive a consistency result for our suggested estimator. In the special case of max-linear models we show furthermore that our procedure provides an alternative way of statistical inference for this class of models. Finally, we provide data examples which show that our method is able to find relevant patterns in extremal observations and allows us to classify extremal events

Transmission network expansion planning with stochastic multivariate load and wind modeling

The increasing penetration of intermittent energy sources along with the introduction of shiftable load elements renders transmission network expansion planning (TNEP) a challenging task. In particular, the ever-expanding spectrum of possible operating points necessitates the consideration of a very large number of scenarios within a cost-benefit framework, leading to computational issues. On the other hand, failure to adequately capture the behavior of stochastic parameters can lead to inefficient expansion plans. This paper proposes a novel TNEP framework that accommodates multiple sources of operational stochasticity. Inter-spatial dependencies between loads in various locations and intermittent generation units' output are captured by using a multivariate Gaussian copula. This statistical model forms the basis of a Monte Carlo analysis framework for exploring the uncertainty state-space. Benders decomposition is applied to efficiently split the investment and operation problems. The advantages of the proposed model are demonstrated through a case study on the IEEE 118-bus system. By evaluating the confidence interval of the optimality gap, the advantages of the proposed approach over conventional techniques are clearly demonstrated