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.
Similar content being viewed by others
REFERENCES
Borch, K. (1974), The Mathematical Theory of Insurance. Lexington: D.C. Heath & Company.
Bowers, N.L., Gerber, H.U., Hickman, J.C., Jones, O.A. and Nesbitt, C.J. (1996), Actuarial Mathematics. Itasca, IL: Society of Actuaries.
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.
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.
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.
De Vylder, F.E. (1996), Advanced Risk Theory. A Self-Contained Introduction. Bruxelles: Editions de l'Université Libre de Bruxelles-Swiss Association of Actuaries.
Fishburn, P.C. (1982a), The Foundations of Expected Utility. Dordrecht: Reidel Publishing Co.
Fishburn, P.C. (1982b), Moment-preserving shifts and stochastic dominance, Mathematics of Operations Research 7: 629-634.
Goovaerts, M.J., Kaas, R., Van Heerwaarden, A.E. and Bauwelinckx, T. (1990), Effective Actuarial Methods. Amsterdam: North-Holland.
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.
Kaas, R., Van Heerwaarden, A.E. and Goovaerts, M.J. (1994), Ordering of Actuarial Risks. Bruxelles: CAIRE Educations Series, vol. 1.
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.
Roberts, A.W. and Varberg, D.E. (1973), Convex Functions. New York: Academic Press.
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.
Schmidt, U. (1998), Axiomatic Utility Theory under Risk. Lecture Notes in Economics and Mathematical Systems 461. Berlin: Springer Verlag.
Shaked, M. and Shanthikumar, J.G. (1994), Stochastic Orders and their Applications. New York: Academic Press.
Trowbridge, C.L. (1989), Fundamental Concepts of Actuarial Sciences, Itasca, IL: Actuarial Education and Research Fund.
Von Neumann, J. and Morgenstern, O. (1947), Theory of Games and Economic Behavior, second edn. Princeton: Princeton University Press.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1023/A:1010336203373