Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-26T22:36:36.128Z Has data issue: false hasContentIssue false
  • English
  • Français

Mean-Value Principle under Cumulative Prospect Theory

Published online by Cambridge University Press:  09 August 2013

Marek Kaluszka  and
Michał Krzeszowiec
Marek Kaluszka
Affiliation:
Institute of Mathematics, Łódź University of Technology, Ul. Wólczańska 215, 90-924 Łódź, Poland, E-mail: kaluszka@p.lodz.pl
Michał Krzeszowiec
Affiliation:
Institute of Mathematics, Łódź University of Technology, Ul. Wólczańska 215, 90-924 Łódź, Poland, E-mail: kaluszka@p.lodz.pl Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa, Poland, E-mail: michalkrzeszowiec@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

In the paper we introduce a generalization of the mean-value principle under Cumulative Prospect Theory. This new method involves some well-known ways of pricing insurance contracts described in the actuarial literature. Properties of this premium principle, such as translation and scale invariance, additivity for independent risks, risk loading and others are studied.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 1 , May 2012 , pp. 103 - 122
Copyright
Copyright © International Actuarial Association 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bernard, C. and Ghossoub, M. (2010) Static portfolio choice under Cumulative Prospect Theory. Mathematics and Financial Economics 2, 277–306.Google Scholar
Denneberg, D. (1994) Lectures on Non-additive Measure and Integral. Kluwer Academic Publishers, Boston.Google Scholar
Gerber, H.U. (1979) An introduction to Mathematical Risk Theory. Homewood, Philadelphia.Google Scholar
Gillen, B.J. and Markowitz, H.M. (2010) A Taxonomy of Utility Functions. Variations in Economic Analysis, Springer New York, 61–69.Google Scholar
De Giorgi, E., Hens, T. and Rieger, M.O. (2009) Financial Market Equilibria with Cumulative Prospect Theory. Swiss Finance Institute Research Paper No. 07-21.Google Scholar
De Giorgi, E. and Hens, T. (2006) Making prospect theory fit for finance. Financial Markets and Portfolio Management 20, 339–360.CrossRefGoogle Scholar
Goldstein, W.M. and Einhorn, H.J. (1987) Expression theory and the preference reversal phenomenon. Psychological Review 94, 236–254.Google Scholar
Goovaerts, M.J., De Vylder, F. and Haezendonck, J. (1984) Insurance Premiums: Theory and Applications. North-Holland, Amsterdam.Google Scholar
Van der Hoek, J. and Sherris, M. (2001) A class of non-expected utility risk measures and implications for asset allocation. Insurance: Mathematics and Economics 28, 69–82.Google Scholar
Kahneman, D. and Tversky, A. (1979) Prospect theory: An analysis of decisions under risk. Econometrica 47, 313–327.Google Scholar
Kaluszka, M. and Okolewski, A. (2008) An extension of Arrow's result on optimal reinsurance contract. Journal of Risk and Insurance 75, 275–288.Google Scholar
Köszegi, B. and Rabin, M. (2007) Reference-Dependent Risk Attitudes. American Economic Review 97, 1047–1073.CrossRefGoogle Scholar
Kuczma, M. (2009) An Introduction to the Theory of Functional Equations and Inequalities. Second edition, Edited by Gilányi, Attila, Birkhäuser. Berlin.Google Scholar
Luan, C. (2001) Insurance premium calculations with anticipated utility theory. ASTIN Bulletin 31, 23–35.Google Scholar
Polyanin, A.D. and Manzhirov, A.H. (2007) Handbook of Mathematics for Engineers and Scientists. Chapman & Hall / CRC Press, Boca Raton – London.Google Scholar
Prelec, D. (1998) The probability weighting function. Econometrica 66, 497–527.Google Scholar
Quiggin, J. (1982) A theory of anticipated utility. Journal of Economic Behavior and Organization 3, 323–343.Google Scholar
Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1999) Stochastic Processes for Insurance and Finance. John Wiley & Sons, New York.Google Scholar
Schmidt, U., Starmer, C. and Sugden, R. (2008) Third-generation prospect theory. Journal of Risk and Uncertainty 36, 203–223.Google Scholar
Schmidt, U. and Zank, H. (2007) Linear cumulative prospect theory with applications to portfolio selection and insurance demand. Decisions in Economics and Finance 30, 1–18.Google Scholar
Segal, U. (1989) Anticipated utility theory: a measure representation approach. Annals of Operations Research 19, 359–373.Google Scholar
Sereda, E.N., Bronshtein, E.M., Rachev, S.T., Fabozzi, F.J., Sun, Wei and Stoyanov, S.V. (2010) Distortion Risk Measures in Portfolio Optimization. In Handbook of Portfolio Construction: Contemporary Applications of Markowitz Techniques. Edited by Guerard, J.B., 649–673.Google Scholar
Teitelbaum, J. (2007) A unilateral accident model under ambiguity. Journal of Legal Studies 36, 431–477.Google Scholar
Tversky, A. and Kahneman, D. (1992) Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty 5, 297–323.Google Scholar
Wakker, P.P. (2010) Prospect Theory: For Risk and Ambiguity. Cambridge University Press.Google Scholar
Wang, S. (1996) Premium calculation by transforming the layer premium density. ASTIN Bulletin 26, 71–92.Google Scholar