791 research outputs found

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

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    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.

    A kaleidoscopic view of multivariate copulas and quasi-copulas

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    A study on multi-level redundancy allocation in coherent systems formed by modules

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    The present work studies the effect of redundancies on the reliability of coherent systems formed by modules. Different redundancies at components’ level versus redundancies at modules’ level are investigated, including active and standby redundancies. For that, a new model is presented. This model takes into account the dependence among the components, as well as, the dependence among the modules of the system. In both cases, the dependence structure is modeled by copula functions. Several results are provided to compare systems consisting of heterogeneous components. The comparisons are distribution-free with respect to the components. In particular, we consider the cases when the components in the modules are independent and connected (or not) in series, and when the components are dependent within the modules. In both cases, it is assumed that the modules can be dependent. Furthermore, the case in which the components in each module are identically distributed (dependent or independent) is also considered. We illustrate the theoretical results with several examplesNT is partially supported by Ministerio de Ciencia e Innovación of Spain under grant PID2019-108079GB-C22/AEI/10.13039/501100011033. AA was supported by Ministerio de Economía y Competitividad of Spain under grant MTM2017-89577-P. Finally, JN is partially supported by Ministerio de Ciencia e Innovación of Spain under grant PID2019-103971GBI00/ AEI/10.13039/50110001103

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

    Get PDF
    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

    Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula?

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    Two approaches may be considered in order to determine the Solvency II economic capital: the use of a standard formula or the use of an internal model (global or partial). However, the results produced by these two methods are rarely similar, since the underlying hypothesis of marginal capital aggregation is not verified by the projection models used by companies. We demonstrate that the standard formula can be considered as a first order approximation of the result of the internal model. We therefore propose an alternative method of aggregation that enables to satisfactorily capture the diversity among the various risks that are considered, and to converge the internal models and the standard formula.
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