Abstract
We examine two important claims by S.S. Wang and J. Treussard concerning the use of distortion functions as a universal tool in pricing financial and insurance risks, and the use of risk neutral probabilities in evaluating risks, respectively. Their claims seem reasonable only in the classical framework of Black–Scholes model, but not convincing in more extended and realistic models such as Lévy processes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Acerbi, C. (2002). Spectral measures of risk: a coherent representation of subjective risk aversion. Journal Banking and Finance, 26(7), 1505–1518.
Artzner, P., Delbaen, F., Elber, J., & Heath, D. (1999). Coherent measures of risk. Mathematical Finance, 9, 203–228.
Artzner, P., Delbaen, F., Eber, J. M., & Heath, D. (2007). Coherent multiperiod risk adjusted values and Bellman’s principle. Annals of Operations Research, 152, 5–22.
Bertoin, J. (1996). Lévy processes. Cambridge: Cambridge University Press.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal Political Economy, 81, 637–654.
Etheridge, A. (2002). A course in financial calculus. Cambridge: Cambridge Univ. Press.
Gerber, H. U., & Shiu, E. S. W. (1994). Option pricing by Esscher transforms. Transactions on Society of Actuaries, 46, 99–191.
Gerber, H. U., & Shiu, E. S. W. (1996). Actuarial bridges to dynamic hedging and option pricing. Insurance: Mathematics and Economics, 18, 183–218.
Grabisch, M., & Labreuche, C. (2010). A decade of applications of the Choquet and Sugeno integrals in multi-criteria decision aid. Annals of Operations Research, 175, 247–286.
Hamada, M., & Sherris, M. (2003). Contingent claim pricing using probability distortion operators. Applied Mathematical Finance, 10(1), 19–47.
Huber, J. P., & Ronchetti, E. M. (2009). Robust statistics. New York: Wiley.
Labreuche, C., & Grabisch, M. (2007). The representation of conditional relative importance between criteria. Annals of Operations Research, 154, 93–122.
Nguyen, H. T. (2006). An introduction to random sets. London/Boca Raton: Chapman & Hall/CRC Press.
Raible, S. (2000). Lévy processes in finance: theory, numerics, and empirical facts. Ph.D. thesis, Freiburg Univ.
Schoutens, W. (2003). Lévy processes in finance: pricing financial derivatives. New York: Wiley.
Sriboonchitta, S., Wong, W. K., Dhompongsa, S., & Nguyen, H. T. (2009). Stochastic dominance and applications to finance, risk and economics. London/Boca Raton: Chapman & Hall/CRC Press.
Treussard, J. (2006). The non-monotonicity of value-at-risk and the validity of risk measures over different horizons, available at: http://ssrn.com/abstract=776651.
Wang, S. S. (2000). A class of distortion operators for pricing financial and insurance risks. Journal of Risk and Insurance, 67(1), 15–36.
Wang, S. S. (2002). A Universal framework for pricing financial and insurance risks. ASTIN Bulletin, 32(2), 231–234.
Wang, S. S. (2003). Equilibrium pricing transforms: new results using Buhlmann’s 1980 economic model. ASTIN Bulletin, 33(1), 57–75.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nguyen, H.T., Pham, U.H. & Tran, H.D. On some claims related to Choquet integral risk measures. Ann Oper Res 195, 5–31 (2012). https://doi.org/10.1007/s10479-011-0848-9
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-011-0848-9