Skip to main content
Log in

On S-Convexity and Risk Aversion

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

The present note first discusses the concept of s-convex pain functions in decision theory. Then, the economic behavior of an agent with such a pain function is represented through the comparison of some recursive lotteries.

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

Access this article

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

  • Borch, K. (1974), The Mathematical Theory of Insurance. Lexington: D.C. Heath & Company.

    Google Scholar 

  • Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, O.A. and Nesbitt, C.J. (1996), Actuarial Mathematics. Itasca, IL: Society of Actuaries.

    Google Scholar 

  • Denuit, M., DeVylder, E. and Lefèvre, Cl. (1999), Extremal generators and extremal distributions for the continuous s-convex stochastic orderings, Insurance: Mathematics and Economics 24: 201-217.

    Google Scholar 

  • Denuit, M., Dhaene, J. and Van Wouwe, M. (1999), The economics of insurance: a review and some recent developments, Bulletin de l'Association Suisse des Actuaires 2: 137-175.

    Google Scholar 

  • Denuit, M., Lefèvre, Cl. and Shaked, M. (1998), The s-convex orders among real random variables, with applications, Mathematical Inequalities and Their Applications 1: 585-613.

    Google Scholar 

  • De Vylder, F.E. (1996), Advanced Risk Theory. A Self-Contained Introduction. Bruxelles: Editions de l'Université Libre de Bruxelles-Swiss Association of Actuaries.

    Google Scholar 

  • Fishburn, P.C. (1982a), The Foundations of Expected Utility. Dordrecht: Reidel Publishing Co.

    Google Scholar 

  • Fishburn, P.C. (1982b), Moment-preserving shifts and stochastic dominance, Mathematics of Operations Research 7: 629-634.

    Google Scholar 

  • Goovaerts, M.J., Kaas, R., Van Heerwaarden, A.E. and Bauwelinckx, T. (1990), Effective Actuarial Methods. Amsterdam: North-Holland.

    Google Scholar 

  • Hürlimann, W. (1998), Extremal Moment Methods and Stochastic Orders. Application in Actuarial Sciences. Monograph manuscript.

  • Kaas, R. and Hesselager, O. (1995), Ordering claim size distributions and mixed Poisson probabilities, Insurance: Mathematics and Economics 17: 193-201.

    Google Scholar 

  • Kaas, R., Van Heerwaarden, A.E. and Goovaerts, M.J. (1994), Ordering of Actuarial Risks. Bruxelles: CAIRE Educations Series, vol. 1.

    Google Scholar 

  • Mosler, K. and Scarsini, M. (1991), Some theory of stochastic dominance. In: K. Mosler and M. Scarsini, eds, Stochastic Orders and Decision under Risk. IMS Lecture Notes 19: 261-284.

  • Pečarić, J.E., Proschan, F. and Tong, Y.L. (1992), Convex Functions, Partial Orderings, and Statistical Applications. New York: Academic Press.

    Google Scholar 

  • Roberts, A.W. and Varberg, D.E. (1973), Convex Functions. New York: Academic Press.

    Google Scholar 

  • Scarsini, M. (1994), Comparing risk and risk aversion. In: M. Shaked and J.G. Shanthikumar, Stochastic Orders and their Applications, 351-378. New York: Academic Press.

    Google Scholar 

  • Schmidt, U. (1998), Axiomatic Utility Theory under Risk. Lecture Notes in Economics and Mathematical Systems 461. Berlin: Springer Verlag.

    Google Scholar 

  • Shaked, M. and Shanthikumar, J.G. (1994), Stochastic Orders and their Applications. New York: Academic Press.

    Google Scholar 

  • Trowbridge, C.L. (1989), Fundamental Concepts of Actuarial Sciences, Itasca, IL: Actuarial Education and Research Fund.

    Google Scholar 

  • Von Neumann, J. and Morgenstern, O. (1947), Theory of Games and Economic Behavior, second edn. Princeton: Princeton University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Denuit, M., Lefèvre, C. & Scarsini, M. On S-Convexity and Risk Aversion. Theory and Decision 50, 239–248 (2001). https://doi.org/10.1023/A:1010336203373

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010336203373

Navigation