Skip to main content
SpringerLink
Log in

Optimal reinsurance under distortion risk measures and expected value premium principle for reinsurer

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper discusses optimal reinsurance strategy by minimizing insurer’s risk under one general risk measure: Distortion risk measure. The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss. An explicit solution of the insurer’s optimal reinsurance problem is obtained. The optimal strategies for some special distortion risk measures, such as value-at-risk (VaR) and tail value-at-risk (TVaR), are also investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cai J, Tan K S, Wang C, and Zhang Y, Optimal reinsurance under VaR and CTE risk measures, Insurance: Mathematics and Economics, 2008, 43(1): 185–196.

    MATH  MathSciNet  Google Scholar 

  2. Cheung K C, Optimal reinsurance revisited —A geometric approach, Astin Bulletin, 2010, 40(1): 221–239.

    Article  MATH  MathSciNet  Google Scholar 

  3. Dhaene J, Vanduffel S, Goovaerts M J, Kaas R, Tang Q, and Vyncke D, Risk measures and comonotonicity: A review, 2006, Stochastic Models, 22: 573–606.

  4. Wang S, A class of distortion operators for pricing financial and insurance risks, Journal of Risk and Insurance, 2000, 67(1): 15–36.

    Article  Google Scholar 

  5. Chi Y and Tan K S, Optimal reinsurance under VaR and CVaR risk measures: A simplified approach, Astin Bulletin, 2011, 41(2): 487–509.

    MATH  MathSciNet  Google Scholar 

  6. Bernard C and Tian W, Optimal reinsurance arrangements under tail risk measures, Journal of Risk and Insurance, 2009, 76(3): 706–725.

    Article  Google Scholar 

  7. Gajek L and Zagrodny D, Reinsurance arrangements maximizing insurer’s survival probability, Journal of Risk and Insurance, 2004, 71(3): 421–435.

    Article  Google Scholar 

  8. Kaluszka M, Optimal reinsurance under convex principles of premium calculation. Insurance: Mathematics and Economics, 2005, 36: 375–398.

    MATH  MathSciNet  Google Scholar 

  9. Kaluszka M and Okolewski A, An extension of Arrow’s result on optimal reinsurance contract, Journal of Risk and Insurance, 2008, 75(2): 275–288.

    Article  Google Scholar 

  10. Cui W, Yang J P, and Wu L, Optimal reinsurance minimizing the distortion risk measure under general reinsurance premium principles, Insurance: Mathematics and Economics, 2013, 53(1): 74–85.

    MATH  MathSciNet  Google Scholar 

  11. Cai J and Wei W, Optimal reinsurance with positively dependent risks, Insurance: Mathematics and Economics, 2012, 50(1): 57–63.

    MATH  MathSciNet  Google Scholar 

  12. Rao M, Measure Theory and Integration, Wiley, New York, 1987.

    MATH  Google Scholar 

  13. Zorich V, Mathematical Analysis I, Springer, Germany, 2004.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Finance, Beijing Technology and Business University, Beijing, 100037, China

    Yanting Zheng

  2. Department of Financial Mathematics, Peking University, Beijing, 100871, China

    Wei Cui

  3. Department of Financial Mathematics, School of Mathematical Sciences and Center of Statistical Science, Peking University, Beijing, 100871, China

    Jingping Yang

Authors
  1. Yanting Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jingping Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanting Zheng.

Additional information

Zheng’s research was supported by the Program of National Natural Science Foundation of Youth of China under Grant No. 11201012 and PHR201007125; Yang’s research was supported by the Key Program of National Natural Science Foundation of China under Grant No. 11131002 and the National Natural Science Foundation of China under Grant No. 11271033.

This paper was recommended for publication by Editor WANG Shouyang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, Y., Cui, W. & Yang, J. Optimal reinsurance under distortion risk measures and expected value premium principle for reinsurer. J Syst Sci Complex 28, 122–143 (2015). https://doi.org/10.1007/s11424-014-2095-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-014-2095-z

Keywords

Search

Navigation