Hierarchical structures in the aggregation of premium risk for insurance underwriting

Savelli, Nino; Clemente, Gian Paolo

doi:10.1080/03461231003703672

Cited by 19 publications

(13 citation statements)

References 5 publications

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“…The method is presented and motivated differently in Sandström (2007), but it is apart from this exactly the same, see also Savelli and Clemente (2011) for a version that is a variation of Sandström's.…”

Section: A Cornish-fisher Methodsmentioning

confidence: 99%

“…It should, like the other one, recreate the correlations in Table 1 to promote insight into the impact of discrepant treatments of tail-dependency. Multiple, hierarchical copula modelling is treated in great generality in Bedford and Cooke (2002) with Aas, Czabo, Frigessi and Bakken (2009) and Savelli and Clemente (2011) contributions in insurance. In Savelli and Clemente (2011) the aggregate distribution has been obtained by assuming a log-normal distribution and by using Hierarchical Copula without any approximation, as both marginal distributions and copula have been generated by Monte Carlo methods.…”

Section: A Simplified Solvency II Insurance Companymentioning

confidence: 99%

“…The log-normal approach can be fortified in this direction through copula constructions at the expense of using a small dose of Monte Carlo in the skewness update. As pointed out in Savelli and Clemente (2011) we are now entering the realm of hierarchical copulas with highly unequal degree of dependence for different groups of variables. To evaluate the accuracy of the log-normal aggregation method in the example in Figure 1 a bottom-up model is needed.…”

Section: Introductionmentioning

confidence: 99%

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Risk aggregation in Solvency II through recursive log-normals

Bølviken

Guillén

2017

Insurance: Mathematics and Economics

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It is argued that the accuracy of risk aggregation in Solvency II can be improved by updating skewness recursively. A simple scheme based on the log-normal distribution is developed and shown to be superior to the standard formula and to adjustments of the Cornish-Fisher type. The method handles tail-dependence if a simple Monte Carlo step is included. A hierarchical Clayton copula is constructed and used to confirm the accuracy of the log-normal approximation and to demonstrate the importance of including tail-dependence. Arguably a log-normal scheme makes the logic in Solvency II consistent, but many other distributions might be used as vehicle, a topic that may deserve further study.JEL codes: G22, G28.

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Section: A Cornish-fisher Methodsmentioning

confidence: 99%

Section: A Simplified Solvency II Insurance Companymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Risk aggregation in Solvency II through recursive log-normals

Bølviken

Guillén

2017

Insurance: Mathematics and Economics

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“…Eling and Holzmüller () as well as Cummins and Phillips () conduct an international comparison of regulatory standards for the insurance industry, and Gisler () contrasts the nonlife risk models embedded in Solvency II and the SST with an emphasis on parameter estimation. Finally, Savelli and Clemente () as well as Christiansen et al () examine the aggregation formula for different risk classes under the Solvency II standard approach, focusing on issues with regard to the underlying correlation matrix as well as the implied diversification effect.…”

Section: Literature Reviewmentioning

confidence: 99%

The Impact of Private Equity on a Life Insurer's Capital Charges Under Solvency II and the Swiss Solvency Test

Braun

Schmeiser

Siegel

2013

J of Risk & Insurance

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In this article, we conduct an in-depth analysis of the impact of private equity investments on the capital requirements faced by a representative life insurance company under Solvency II as well as the Swiss Solvency Test. Our discussion begins with an empirical performance measurement of the asset class over the period from 2001 to 2010, suggesting that limited partnership private equity funds may be suited for the purpose of portfolio enhancement. Subsequently, we review the market risk standard approaches set out by both regulatory regimes and outline a potential framework for an internal model. Based on an implementation of these solvency models, it is possible to demonstrate that private equity is overly penalized by the standard approaches. Hence, life insurers aiming to exploit the asset class's return potential may expect significantly lower capital charges when applying an economically sound internal model. Finally, we show that, from a regulatory capital perspective, it can even be less costly to increase the exposure to private rather than public equity. and caroline.siegel@unisg.ch, respectively. We are grateful to two anonymous referees as well as Karin Jans, Andy Hawson, and Joerg Allenspach of Swiss Re for their helpful comments and suggestions.

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“…We limited the analysis to this simple choice of copula having at its disposal correlation coefficient provided by the Standard Formula, but the evaluation may be properly extended in order to consider both a more significant tail dependency between several LoBs and hierarchical structure based on Archimedean Copulas to aggregate LoBs (see at this regard [21]). Despite the positive correlation provided by Solvency II, we observe in Table 4 a, diversification effect between LoBs.…”

Section: Numerical Analysismentioning

confidence: 99%

The Impact of Reinsurance Strategies on Capital Requirements for Premium Risk in Insurance

Clemente

Savelli

Zappa

2015

Risks

Self Cite

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New risk-based solvency requirements for insurance companies across European markets have been introduced by Solvency II and will come in force from 1 January 2016. These requirements, derived by a Standard Formula or an Internal Model, will be by far more risk-sensitive than the required solvency margin provided by the current legislation. In this regard, a Partial Internal Model for Premium Risk is developed here for a multi-line NonLife insurer. We follow a classical approach based on a Collective Risk Model properly extended in order to consider not only the volatility of aggregate claim amounts but also expense volatility. To measure the effect of risk mitigation, suitable reinsurance strategies are pursued. We analyze how naï ve coverage as conventional Quota Share and Excess of Loss reinsurance may modify the exact moments of the distribution of technical results. Furthermore, we investigate how alternative choices of commission rates in proportional treaties may affect the variability of distribution. Numerical results are also figured out in the last part of the paper with evidence of different effects for small and large companies. The main reasons for these differences are pointed out.

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Hierarchical structures in the aggregation of premium risk for insurance underwriting

Cited by 19 publications

References 5 publications

Risk aggregation in Solvency II through recursive log-normals

Risk aggregation in Solvency II through recursive log-normals

The Impact of Private Equity on a Life Insurer's Capital Charges Under Solvency II and the Swiss Solvency Test

The Impact of Reinsurance Strategies on Capital Requirements for Premium Risk in Insurance

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