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2022 | 14 | nr 4 | 381--413
Tytuł artykułu

Study of Actuarial Characteristics of One-Year and Ultimate Reserve Risk Distributions Based on Market Data

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this work, we perform an analysis of the characteristics of the one-year and ultimate reserve risk distributions commonly used in actuarial science: duration, first development factor, coefficient of variation, skewness coefficient, skewness-to-CoV ratio, emergence factor, emergence pattern, and risk margin run-off patterns. Our study is based on empirical data for two European markets: the Polish and Slovak markets. We provide benchmarks and ranges for the considered characteristics, as well as analyse the relations between them. We study Solvency II lines of business and compare our coefficients of variation to the Standard Formula reserve risk standard deviations. We investigate more deeply the topic of emergence pattern and risk margin run-off patterns. (original abstract)
Rocznik
Tom
14
Numer
Strony
381--413
Opis fizyczny
Twórcy
  • SGH Warsaw School of Economics, Poland; ERGO Hestia SA
Bibliografia
  • [1] AISAM-ACME, (2007), AISAM-ACME study on non-life long tail liabilities: Reserve risk and risk margin assessment under Solvency II, available at: https: //www.amice-eu.org/.
  • [2] ASTIN, (2016), ASTIN Working Party on Non-Life Reserving Practices.
  • [3] Bird C., Cairns M., (2011), Practical experiences of modelling one-year risk emergence, GIRO Conference and Exhibition 2011.
  • [4] Buchwalder M., Bühlmann H., Merz M., Wüthrich M., (2006), The Mean Square Error of Prediction in the Chain Ladder Reserving Method (Mack and Murphy Revisited), ASTIN Bulletin 36, 521-42.
  • [5] CEIOPS, (2010), Solvency II Calibration Paper. CEIOPS-SEC-40-10, 15 April 2010.
  • [6] Chan K., Ramyar M., (2016), Practical Challenges in Reserve Risk, Institute and Faculty of Actuaries, available at: https://www. actuaries.org.uk/system/files/field/document/Plenary 3 - Practical Challenges in Reserve Risk_0.pdf.
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  • [8] Dal Moro E., (2012), An Approximation of the Non-Life Reserve Risk Distribution Using the Cornish-Fisher Expansion. Available at SSRN: https: //papers.ssrn.com/sol3/papers.cfm?abstract_id=2965384.
  • [9] Dal Moro E., Krvavych Y., (2017), Probability of Sufficiency of Solvency II Reserve Risk Margins: Practical Approximations, ASTIN Bulletin 47(3), 737785.
  • [10] EIOPA, (2011), Calibration of the Premium and Reserve Risk Factors in Standard Formula of Solvency II. EIOPA 11/163, available at: https://register.eiopa.europa.eu/Publications/Reports/EIOPA-11-163-A-Report_JWG_on_NL_and_Health_non-SLT_Calibration.pdf.
  • [11] EIOPA, (2019), Answer to Q&A (Question ID: 1769), available at: https: //www.eiopa.europa.eu/content/1769_en.
  • [12] EIOPA, (2020), European Insurance Overview 2020, available at: https:// www.eiopa.europa.eu/content/european-insurance-overview-2020.
  • [13] England P., Cairns M., Scarth R., (2012), The 1 year view of reserving risk: The "actuary-in-the-box" vs. emergence patterns, GIRO Conference and Exhibition 2012.
  • [14] England P., Verrall R. J., Wüthrich M., (2019), On the lifetime and one-year views of reserve risk, with application to IFRS 17 and Solvency II risk margins, Insurance: Mathematics and Economics 85, 74-88.
  • [15] Gesmann M. et al. (2021), Package "Chain Ladder", R Vignette.
  • [16] Gisler A., (2019), The Reserve Uncertainties in the Chain-Ladder model of Mack revisited, ASTIN Bulletin 49, 787-821.
  • [17] Guy Carpenter, (2014), Insurance Risk Benchmark Review. Annual Statistical Review.
  • [18] Institute of Actuaries, (2002), Claims Reserving Working Party Paper, available at: https://www.actuaries.org.uk/system/files/documents/pdf/lyons. pdf.
  • [19] ISVAP, (2006), Reserve Requirements and Capital Requirements in Non-Life Insurance: An analysis of the Italian MTPL insurance market by stochastic claims reserving models.
  • [20] KNF, (2020), Claims development factors according to data from 31st December 2019. Urząd Komisji Nadzoru Finansowego (Polish Financial Supervision Authority). Departament Nadzoru Ubezpieczeniowego i Monitorowania Ryzyk. Warszawa, 17th December 2020. Available at: https://www.knf.gov.pl/ ?articleId=72000&p_id=18.
  • [21] Mack T., (1993), Distribution-free calculation of the standard error of chain ladder reserve estimates, ASTIN Bulletin 23(2), 213-225.
  • [22] Mack T., (1994), Measuring the variability of chain-ladder reserve estimates, Casualty Actuarial Society Forum I, 101-182.
  • [23] NBS, (2020), S.19.01.01 Non-life insurance claims, available at: https://nbs.sk/_img/Documents/_Dohlad/ORM/Poistovnictvo/EN_ trojuholniky_SPOLU_N_2019.xlsx.
  • [24] Ohlsson E., Lauzeningks J., (2009), The one-year non-life insurance risk, Insurance: Mathematics and Economics 45, 203-8.
  • [25] Scarth R., Jain S., Cerchiara R. R., (2020), A Practitioner's Introduction to Stochastic Reserving: The One-Year View. Institute and Faculty of Actuaries.
  • [26] 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).
  • [27] Szatkowski M., Delong Ł., (2021), One-Year and Ultimate Reserve Risk in Mack Chain Ladder Model, Risks 9(9):152, available at: https://www.mdpi.com/ 2227-9091/9/9/152.
  • [28] Wüthrich M.V., Merz M., (2008), Modelling the Claims Development Result for Solvency Purposes, Casualty Actuarial Society E-Forum, Fall 2008, 542-568.
  • [29] Wüthrich M.V., Merz M., (2015), Claims run-off uncertainty: the full picture, Swiss Finance Institute Research Paper No. 14-69.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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