218
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Representation of concave distortions and applications

Pages 768-783 | Received 14 Jan 2019, Accepted 22 Apr 2019, Published online: 11 May 2019

References

  • Acerbi, C. (2002). Spectral measures of risk: a coherent representation of subjective risk aversion. Journal of Banking & Finance 26(7), 1505–1518. doi: 10.1016/S0378-4266(02)00281-9
  • Aczél, J. (1966). Lectures on functional equations and their applications. New York: Academic Press.
  • Artzner, P., Delbaen, F., Eber, J. M. & Heath, D. (1999). Coherent measures of risk. Mathematical Finance 9(3), 203–228. doi: 10.1111/1467-9965.00068
  • Bagnoli, M. & Bergstrom, T. (2005). Log-concave probability and its applications. Economic Theory 26(2), 445–469. doi: 10.1007/s00199-004-0514-4
  • Bannör, K. F. & Scherer, M. (2014). On the calibration of distortion risk measures to bid-ask prices. Quantitative Finance 14(7), 1217–1228. doi: 10.1080/14697688.2014.887220
  • Bernardo, A. E. & Ledoit, O. (2000). Gain, loss, and asset pricing. Journal of Political Economy 108(1), 144–172. doi: 10.1086/262114
  • Cherny, A. S. & Madan, D. B. (2009). New measures for performance evaluation. Review of Financial Studies 22(7), 2571–2606. doi: 10.1093/rfs/hhn081
  • Daykin, C. D., Pentikainen, T. & Pesonen, M. (1994). Practical risk theory for actuaries. London: Chapman and Hall.
  • Dharmadhikari, S. & Joag-Dev, K. (1988). Unimodality, convexity, and applications. New York: Academic Press.
  • Föllmer, H. & Schied, A. (2011). Stochastic finance: an introduction in discrete time. Berlin: Walter de Gruyter.
  • Kusuoka, S. (2001). On law invariant coherent risk measures. In Advances in Mathematical Economics. Tokyo: Springer. P. 83–95.
  • Pichler, A. (2013). The natural Banach space for version independent risk measures. Insurance: Mathematics and Economics 53(2), 405–415.
  • Rockafellar, R. T. (1970). Convex analysis. Princeton: University Press.
  • Rolski, T., Schmidli, H., Schmidt, V. & Teugels, J. L. (2009). Stochastic processes for insurance and finance (Vol. 505). Chichester: John Wiley & Sons.
  • Straub, E. (1988). Non-life insurance mathematics. Berlin: Springer.
  • Tsanakas, A. (2004). Dynamic capital allocation with distortion risk measures. Insurance: Mathematics and Economics 35(2), 223–243.
  • Tsukahara, H. (2009). One-parameter families of distortion risk measures. Mathematical Finance 19(4), 691–705. doi: 10.1111/j.1467-9965.2009.00385.x
  • Wang, S. (1995). Insurance pricing and increased limits ratemaking by proportional hazards transforms. Insurance Mathematics & Economics 17(1), 43–54. doi: 10.1016/0167-6687(95)00010-P
  • Wang, S. (1996). Premium calculation by transforming the layer premium density. ASTIN Bulletin: The Journal of the IAA 26(1), 71–92. doi: 10.2143/AST.26.1.563234
  • Wang, S. S. (2000). A class of distortion operators for pricing financial and insurance risks. Journal of Risk and Insurance 67, 15–36. doi: 10.2307/253675

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.