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On the robust stability of pricing models for non-life insurance products

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Abstract

One of the most significant and challenging problems in actuarial practice, especially for general insurance, is the modelling of the premium pricing process and furthermore its stability. The classical actuarial approach to calculating the premium simply covers the expected claims, with an increase for eventual expected surplus, chosen such that the portfolio can be considered stable. In this paper, we present an alternative model for the premium pricing process of a portfolio consisting of different non-life products. Moreover, a standard decision function for the determination of the premium is proposed based on the recent claim experience and a negative feedback mechanism of the known surplus value. The investigation of the robust stability of the system is performed via a Linear Matrix Inequality (LMI) criterion, permitting extensions of existing results. The novelty of the approach consists in the use of tools from the robust analysis of engineering systems in the insurance pricing process of non‐life products into a discrete-time framework.

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References

  1. Ackman RC, Green PAG, Young AG (1985) Estimating claims outstanding. General Insurance Monograph, Actuarial Education Senate, Oxford

    Google Scholar 

  2. Balzer LA, Benjamin S (1980) Dynamic response of insurance systems with delayed profit/loss sharing feedback to isolated unpredicted claims. J Inst Actuar 107:513–528

    Article  Google Scholar 

  3. Balzer LA (1982) Control of insurance systems with delayed profit/loss sharing feedback and persisting unpredicted claims. J Inst Actuar 109:285–316

    Article  Google Scholar 

  4. Booth P, Chadburn R, Cooper D, Haberman S, James D (1999) Modern actuarial theory and practice. Chapman & Hall CRC, USA

    MATH  Google Scholar 

  5. Borch K (1967) The theory of risk, Journal of the Royal Statistical Society (Ser. B) Vol. 29, pp 432–452

  6. Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM Studies in Applied Mathematics, SIAM, Philadelphia

    Book  MATH  Google Scholar 

  7. De Finetti B (1957) Su una impostazione alternativa della theoria collectiva del rischio, Transactions of the 15th International Congress of Actuaries. New York II:433–443

    Google Scholar 

  8. Gahinet P, Nemirovski A, Laub A, Chilali M (1995) LMI control toolbox: for use with MATLAB. User’s Guide, The Math Works Inc, USA

    Google Scholar 

  9. Gu K, Kharitonov VL, Chen J (2003) Stability of time-delay systems. Birkhäuser Publications, USA

    Book  MATH  Google Scholar 

  10. Kaas R, Goovaerts M, Dhaene J, Denuit M (2002) Modern actuarial risk theory. Kluwer Academic Publishers, USA

    Google Scholar 

  11. Martin-Löf A (1983) Premium control in an insurance system, an approach using linear control theory. Scand Actuar J 1983(1):1–27

    Article  MATH  Google Scholar 

  12. Martin-Löf A (1994) Lectures on the use of control theory in insurance. Scand Actuar J 1994(1):1–25

    Article  MATH  Google Scholar 

  13. Pantelous AA, Frangos NE, Zimbidis AA (2009) Optimal premium pricing for a heterogeneous portfolio of insurance risks. J Probab Stat 1–18

  14. Vandebroek M, Dhaene J (1990) Optimal premium control in a non-life insurance business. Scand Actuar J 1990(1–2):3–13

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang Y, Xie L, de Souza CE (1992) Robust control of a class of uncertain nonlinear systems. Syst Control Lett 19:139–149

    Article  Google Scholar 

  16. Xu S, Lam J (2008) A survey of linear matrix inequality techniques in stability analysis of delay systems. Int J Syst Sci 39(12):1095–1113

    Article  MathSciNet  MATH  Google Scholar 

  17. Zaks Y, Frostig E, Levikson B (2006) Optimal pricing of a heterogeneous portfolio for a given risk level. ASTIN Bulletin 36(1):161–185

    Article  MathSciNet  MATH  Google Scholar 

  18. Zimbidis A, Haberman S (2001) The combined effect of delay and feedback on the insurance pricing process: a control theory approach. Insur Math Econ 28:263–280

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We are really very grateful to Dr. Leonidas Dritsas (University of Patras, Greece) for the support that he gave us with his expertise in the LMI approaches and algorithms (robust control), and Dr. Alexandros Zimbidis (Athens University of Economics and Business, Greece) for the preliminary discussion of this paper, which actually has been based on his work with Prof. Steven Haberman (City Cass School, London, UK), see references.

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Authors and Affiliations

  1. Institute for Financial and Actuarial Mathematics (IFAM), Department of Mathematical Sciences and Institute for Risk and Uncertainty, University of Liverpool, Liverpool, L69 7ZL, UK

    Athanasios A. Pantelous

  2. School of Engineering and Mathematical Sciences, City University, London, UK

    Athanasios Papageorgiou

Authors
  1. Athanasios A. Pantelous
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  2. Athanasios Papageorgiou
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Correspondence to Athanasios A. Pantelous.

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Pantelous, A.A., Papageorgiou, A. On the robust stability of pricing models for non-life insurance products. Eur. Actuar. J. 3, 535–550 (2013). https://doi.org/10.1007/s13385-013-0074-8

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  • DOI: https://doi.org/10.1007/s13385-013-0074-8

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