Capital Reduction

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Ivan Granito - One of the best experts on this subject based on the ideXlab platform.

  • Capital allocation and RORAC optimization under solvency 2 standard formula
    Annals of Operations Research, 2020
    Co-Authors: Fabio Baione, Paolo Angelis, Ivan Granito
    Abstract:

    Solvency II Directive 2009/138/EC requires an insurance and reinsurance undertakings assessment of a Solvency Capital Requirement by means of the so-called “Standard Formula” or by means of partial or full internal models. Focusing on the first approach, the bottom-up aggregation formula proposed by the regulator allows for a Capital Reduction due to the diversification effect, according to the typical subadditivity property of risk measures. However, once the overall Capital has been assessed no specific allocation formula is provided or required in order to evaluate the contribution of each risk source on the overall Solvency Capital Requirement. The aim of this paper is twofold. First, we provide a closed formula for Capital allocation fully compliant with the Solvency II Capital Requirement assessed by means of the Standard Formula. The solution enables a top-down approach to assess the allocated Solvency Capital Requirement among the risks considered in the Solvency II multilevel aggregation scheme; we demonstrate that the allocation formula adopted is consistent with the Euler allocation principle. Second, a solution is found as a result of an optimum Capital allocation problem based on a Return On Risk Adjusted Capital measure; we establish the equivalence between the Return On Risk Adjusted Capital optimization, when the risk adjusted Capital is calculated according to the Standard Formula, and the Markowitz mean-variance optimization.

  • On a Capital allocation principle coherent with the Solvency 2 standard formula
    arXiv: Risk Management, 2018
    Co-Authors: Fabio Baione, Paolo Angelis, Ivan Granito
    Abstract:

    Solvency II Directive 2009/138/EC requires an insurance and reinsurance undertakings assessment of a Solvency Capital Requirement by means of the so-called "Standard Formula" or by means of partial or full internal models. Focusing on the first approach, the bottom-up aggregation formula proposed by the regulator permits a Capital Reduction due to diversification effect, according to the typical subadditivity property of risk measures. However, once the overall Capital has been assessed no specific allocation formula is provided or required in order to evaluate the contribution of each risk source on the overall SCR. The aim of this paper is to provide a closed formula for Capital allocation fully coherent with the Solvency II Capital Requirement assessed by means of Standard Formula. The solution proposed permits a top-down approach to assess the allocated SCR among the risks considered in the multilevel aggregation scheme established by Solvency II. Besides, we demonstrate that the allocation formula here proposed is consistent with the Euler's allocation principle

Guan-wei Chiou - One of the best experts on this subject based on the ideXlab platform.

Fabio Baione - One of the best experts on this subject based on the ideXlab platform.

  • Capital allocation and RORAC optimization under solvency 2 standard formula
    Annals of Operations Research, 2020
    Co-Authors: Fabio Baione, Paolo Angelis, Ivan Granito
    Abstract:

    Solvency II Directive 2009/138/EC requires an insurance and reinsurance undertakings assessment of a Solvency Capital Requirement by means of the so-called “Standard Formula” or by means of partial or full internal models. Focusing on the first approach, the bottom-up aggregation formula proposed by the regulator allows for a Capital Reduction due to the diversification effect, according to the typical subadditivity property of risk measures. However, once the overall Capital has been assessed no specific allocation formula is provided or required in order to evaluate the contribution of each risk source on the overall Solvency Capital Requirement. The aim of this paper is twofold. First, we provide a closed formula for Capital allocation fully compliant with the Solvency II Capital Requirement assessed by means of the Standard Formula. The solution enables a top-down approach to assess the allocated Solvency Capital Requirement among the risks considered in the Solvency II multilevel aggregation scheme; we demonstrate that the allocation formula adopted is consistent with the Euler allocation principle. Second, a solution is found as a result of an optimum Capital allocation problem based on a Return On Risk Adjusted Capital measure; we establish the equivalence between the Return On Risk Adjusted Capital optimization, when the risk adjusted Capital is calculated according to the Standard Formula, and the Markowitz mean-variance optimization.

  • On a Capital allocation principle coherent with the Solvency 2 standard formula
    arXiv: Risk Management, 2018
    Co-Authors: Fabio Baione, Paolo Angelis, Ivan Granito
    Abstract:

    Solvency II Directive 2009/138/EC requires an insurance and reinsurance undertakings assessment of a Solvency Capital Requirement by means of the so-called "Standard Formula" or by means of partial or full internal models. Focusing on the first approach, the bottom-up aggregation formula proposed by the regulator permits a Capital Reduction due to diversification effect, according to the typical subadditivity property of risk measures. However, once the overall Capital has been assessed no specific allocation formula is provided or required in order to evaluate the contribution of each risk source on the overall SCR. The aim of this paper is to provide a closed formula for Capital allocation fully coherent with the Solvency II Capital Requirement assessed by means of Standard Formula. The solution proposed permits a top-down approach to assess the allocated SCR among the risks considered in the multilevel aggregation scheme established by Solvency II. Besides, we demonstrate that the allocation formula here proposed is consistent with the Euler's allocation principle

Yung-cheng Huang - One of the best experts on this subject based on the ideXlab platform.

Paolo Angelis - One of the best experts on this subject based on the ideXlab platform.

  • Capital allocation and RORAC optimization under solvency 2 standard formula
    Annals of Operations Research, 2020
    Co-Authors: Fabio Baione, Paolo Angelis, Ivan Granito
    Abstract:

    Solvency II Directive 2009/138/EC requires an insurance and reinsurance undertakings assessment of a Solvency Capital Requirement by means of the so-called “Standard Formula” or by means of partial or full internal models. Focusing on the first approach, the bottom-up aggregation formula proposed by the regulator allows for a Capital Reduction due to the diversification effect, according to the typical subadditivity property of risk measures. However, once the overall Capital has been assessed no specific allocation formula is provided or required in order to evaluate the contribution of each risk source on the overall Solvency Capital Requirement. The aim of this paper is twofold. First, we provide a closed formula for Capital allocation fully compliant with the Solvency II Capital Requirement assessed by means of the Standard Formula. The solution enables a top-down approach to assess the allocated Solvency Capital Requirement among the risks considered in the Solvency II multilevel aggregation scheme; we demonstrate that the allocation formula adopted is consistent with the Euler allocation principle. Second, a solution is found as a result of an optimum Capital allocation problem based on a Return On Risk Adjusted Capital measure; we establish the equivalence between the Return On Risk Adjusted Capital optimization, when the risk adjusted Capital is calculated according to the Standard Formula, and the Markowitz mean-variance optimization.

  • On a Capital allocation principle coherent with the Solvency 2 standard formula
    arXiv: Risk Management, 2018
    Co-Authors: Fabio Baione, Paolo Angelis, Ivan Granito
    Abstract:

    Solvency II Directive 2009/138/EC requires an insurance and reinsurance undertakings assessment of a Solvency Capital Requirement by means of the so-called "Standard Formula" or by means of partial or full internal models. Focusing on the first approach, the bottom-up aggregation formula proposed by the regulator permits a Capital Reduction due to diversification effect, according to the typical subadditivity property of risk measures. However, once the overall Capital has been assessed no specific allocation formula is provided or required in order to evaluate the contribution of each risk source on the overall SCR. The aim of this paper is to provide a closed formula for Capital allocation fully coherent with the Solvency II Capital Requirement assessed by means of Standard Formula. The solution proposed permits a top-down approach to assess the allocated SCR among the risks considered in the multilevel aggregation scheme established by Solvency II. Besides, we demonstrate that the allocation formula here proposed is consistent with the Euler's allocation principle