Actuarial Improvements of Standard Formula for Non-life Underwriting Risk

  • Gian Paolo Clemente
  • Nino Savelli


Solvency II Directive introduced a new framework in order to develop new risk management practices to manage risk and to define a minimum capital requirement. To this aim, Commission Delegated Regulation provided the final version of the standard formula. Capital requirement is obtained via a modular structure where each source of risk must be first measured and then aggregated under a linear correlation assumption. As the results of main Quantitative Impact Studies have shown, premium and reserve risks represent a key driver for non-life insurers. In this regard, we focus here on the valuation of the capital requirement for this specific sub-module. Some inconsistencies of the approach provided by Solvency II will be highlighted. We show that some assumptions of the standard formula may lead to an underestimation of the capital requirement for small insurers.


Solvency II Premium and reserve risk Capital requirement Size factor 


  1. Beard, R. E., Pentikäinen, T., & Pesonen, E. (1984). Risk theory (3rd ed.). London: Chapman and Hall.CrossRefGoogle Scholar
  2. Clemente, G. P., & Savelli, N. (2013). Internal Model Techniques of premium and reserve risk for non-life insurers. Mathematical Methods in Economics and Finance, 8(1), 21–34.Google Scholar
  3. Clemente, G. P., Savelli, N., & Zappa, D. (2015). The impact of reinsurance strategies on capital requirements for premium risk in insurance. Risks, 3(2), 164–182.CrossRefGoogle Scholar
  4. Daykin, C., Pentikäinen, T., & Pesonen, M. (1994). Practical risk theory for actuaries. Monographs on statistics and applied probability (Vol. 53). London: Chapman and Hall.Google Scholar
  5. Diers, D. (2009). Stochastic re-reserving in multi-year internal models. Helsinki: Astin Colloquium.Google Scholar
  6. EIOPA. (2011). Report of the Task Force on expected profits arising from future premiums.Google Scholar
  7. EIOPA. (2016). Discussion Paper on the review of specific items in the Solvency II Delegated Regulation.Google Scholar
  8. England, P. (2002). Addendum to “Analytic and bootstrap estimates of prediction errors in claims reserving”. Insurance Mathematics and Economics, 31, 461–466.CrossRefGoogle Scholar
  9. England, P., & Verrall, R. (2002). Stochastic claims reserving in general insurance. British Actuarial Journal, 8(3), 443–544.CrossRefGoogle Scholar
  10. European Commission. (2009). Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II) (Text with EEA relevance).Google Scholar
  11. European Commission. (2010). Quantitative Impact Study 5—Technical Specifications.Google Scholar
  12. European Commission. (2015). Commission Delegated Regulation (EU) 2015/35 supplementing Directive 2009/138/EC of the European Parliament and of the Council on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II). Official Journal of the EU, Vol. 58.Google Scholar
  13. Gisler, A. (2009). The insurance risk in the SST and in Solvency II: Modelling and parameter estimation. Astin Colloquium, 1–4 June 2009, Helsinki.Google Scholar
  14. Klugman, S., Panjer, H. H., & Wilmot, G. E. (2008). Loss models: From data to decisions (3rd ed.). Wiley Series in Probability and Statistics, John Wiley & Sons, Hoboken, New Jersey.Google Scholar
  15. Ohlsonn, E., & Lauzenings, J. (2008). The one-year non-life insurance risk. Manchester: Astin Colloquium.Google Scholar
  16. Savelli, N., & Clemente, G. P. (2009). Modelling aggregate non-life underwriting risk: Standard formula vs internal model. Giornale dell’Istituto Italiano degli Attuari, LXXII(1–2), 301–338.Google Scholar
  17. Savelli, N., & Clemente, G. P. (2011). Hierarchical structures in the aggregation of premium risk for insurance underwriting. Scandinavian Actuarial Journal, (3), 193–213.Google Scholar
  18. Wüthrich, M. V., & Merz, M. (2008, Fall). Modelling the claims development results for solvency purposes. In Casualty Actuarial Society E-Forum (pp. 542–568).Google Scholar

Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Gian Paolo Clemente
    • 1
  • Nino Savelli
    • 1
  1. 1.Department of Mathematics, Finance and EconometricsCatholic UniversityMilanItaly

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