SpringerLink
Log in

Characterization of positive homogeneity for the principle of equivalent utility

  • Original Paper
  • Published:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We establish a characterization of positive homogeneity for the principle of equivalent utility under cumulative prospect theory. The characterization involves not only a form of the utility function, but also a relation between probability weighting functions for gains and losses.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Balbás, A., Balbás, R.: Minimax strategies and duality with applications in financial mathematics. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A. Mat. 105, 291–303 (2011)

  2. Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, D.A., Nesbitt, C.J.: Actuarial Mathematics. The Society of Actuaries, Itasca, Illinois (1986)

    MATH  Google Scholar 

  3. Bühlmann, H.: Mathematical Models in Risk Theory. Springer, New York (1970)

    MATH  Google Scholar 

  4. Centeno, M.L., Simoes, O.: Optimal reinsurance. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A. Mat. 103, 387–405 (2009)

  5. Chudziak, J.: On existence and uniqueness of the principle of equivalent utility under Cumulative Prospect Theory. Insurance: Mathematics and Economics 79, 243–246 (2018)

  6. Chudziak, J.: Extension problems for principles of equivalent utility. Aequationes Math. 93, 217–238 (2019)

    Article  MathSciNet  Google Scholar 

  7. Chudziak, J.: On positive homogeneity and comonotonic additivity of the principle of equivalent utility under Cumulative Prospect Theory. Insur. Math. Econ. 94, 154–159 (2020)

  8. Denneberg, D.: Lectures on Non-Additive Measure and Integral. Kluwer Academic, Boston (1994)

    Book  Google Scholar 

  9. Denuit, M., Dhaene, J., Goovaerts, M., Kaas, R.: Actuarial Theory for Dependent Risks: Measures, Orders and Models. Wiley, Amsterdam (2006)

  10. Diestel, J., Uhl, J.: Vector measures. Mathematical Surveys, No. 15, American Mathematical Society (1977)

  11. Föllmer, H., Schied, A.: Convex measures of risk and trading constraints. Financ. Stochast. 6, 429–447 (2002)

    Article  MathSciNet  Google Scholar 

  12. Goovaerts, M., De Vylder, F., Haezendonck, J.: Insurance Premiums. North-Holland, Theory and Applications (1984)

    MATH  Google Scholar 

  13. Goovaerts M., Kaas R., Laeven R.: A note on additive risk measures in rank-dependent utility. Insur. Math. Econ. 47, 187–189 (2010)

  14. Heilpern, S.: A rank-dependent generalization of zero utility principle. Insur. Math. Econ. 33, 67–73 (2003)

  15. Kaas, R., Goovaerts, M., Dhaene, J., Denuit, M.: Modern Actuarial Risk Theory. Springer, Berlin (2008)

    Book  Google Scholar 

  16. Kahneman, D., Tversky, A.: Prospect theory: an analysis of decision under risk. Econometrica 47, 263–291 (1979)

    Article  MathSciNet  Google Scholar 

  17. Kałuszka, M., Krzeszowiec, M.: Pricing insurance contracts under cumulative prospect theory. Insur. Math. Econ. 50, 159–166 (2012)

  18. Kałuszka, M., Krzeszowiec, M.: On iterative premium calculation principles under cumulative prospect theory. Insur. Math. Econ. 52, 435–440 (2013)

  19. Kuczma, M.: An Introduction to the Theory of Functional Equations and Inequalities. Cauchy’s equation and Jensen’s inequality. Birkhäuser, Berlin (2009)

    Book  Google Scholar 

  20. Nakano, Y.: Efficient hedging with coherent risk measure. J. Math. Anal. Appl. 293, 345–354 (2004)

    Article  MathSciNet  Google Scholar 

  21. Reich, A.: Homogeneous premium calculation principles. ASTIN. Bulletin 14, 122–133 (1984)

    Google Scholar 

  22. Ruszczyński, A., Shapiro, A.: Optimization of convex risk functions. Math. Oper. Res. 31, 433–452 (2006)

    Article  MathSciNet  Google Scholar 

  23. Rolski, T., Schmidli, H., Schmidt, V., Teugels, J.: Stochastic Processes for Insurance and Finance. Wiley, New York (1999)

    Book  Google Scholar 

  24. Sobek, B.: Pexider equation on a restricted domain. Demonstr. Math. 43, 81–88 (2010)

    MathSciNet  MATH  Google Scholar 

  25. Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertain. 5, 297–323 (1992)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Rzeszów, Pigonia 1, 35-310, Rzeszów, Poland

    Jacek Chudziak

Authors
  1. Jacek Chudziak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacek Chudziak.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chudziak, J. Characterization of positive homogeneity for the principle of equivalent utility. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 116, 127 (2022). https://doi.org/10.1007/s13398-022-01269-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s13398-022-01269-7

Keywords

Mathematics Subject Classification

Search

Navigation