Introduction to the Premium Principle Based on the Wang Transform

  • Shingo Saito
Part of the Mathematics for Industry book series (MFI, volume 5)


This is a self-contained introductory survey article on the premium principle based on the Wang transform. We give the definition and examples of the Wang transform and prove that the induced premium principle is a coherent risk measure.


Premium principle Wang transform Risk measure Coherent risk measure 


  1. 1.
    H. Föllmer, A. Schied, Stochastic Finance, extended edn. An Introduction in Discrete Time (Walter de Gruyter & Co., Berlin, 2011)Google Scholar
  2. 2.
    D.B. Owen, A table of normal integrals. Communications in Statistics. B. Simul. Comput. 9(4), 389–419 (1980). doi: 10.1080/03610918008812164
  3. 3.
    S. Wang, Premium calculation by transforming the layer premium density. ASTIN Bulletin 26(1), 71–92 (1996).
  4. 4.
    S. Wang, A class of distortion operators for pricing financial and insurance risks. J. Risk Insur. 67(1), 15–36 (2000). doi: 10.2307/253675 CrossRefGoogle Scholar
  5. 5.
    S.S. Wang, A universal framework for pricing financial and insurance risks. ASTIN Bulletin 32(2), 213–234 (2002).
  6. 6.
    S.S. Wang, V.R. Young, H.H. Panjer, Axiomatic characterization of insurance prices. Insur. Math. Econ. 21(2), 173–183 (1997). doi: 10.1016/S0167-6687(97)00031-0 MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    V.R. Young, Premium Principles, ed. by J. Teugels, B. Sundt (eds.) Encyclopedia of Actuarial Science. (Wiley, New York, 2004), pp. 1322–1331.

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Faculty of Arts and ScienceKyushu UniversityFukuokaJapan

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