×

Axiomatic characterization of insurance prices. (English) Zbl 0959.62099

Summary: We take an axiomatic approach to characterize insurance prices in a competitive market setting. We present four axioms to describe the behavior of market insurance prices. From these axioms it follows that the price of an insurance risk has a Choquet integral representation with respect to a distorted probability [M.E. Yaari, Econometrica 55, 95–115 (1987; Zbl 0616.90005)]. We propose an additional axiom for reducing compound risks. This axiom determines that the distortion function is a power function.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)

Citations:

Zbl 0616.90005
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Aczél, J., On applications and theory of functional equations, (1969), Academic Press New York · Zbl 0176.12801
[2] Albrecht, P., Discussion of G.G. Venter’s premium calculation without arbitrage, ASTIN bulletin, 22, 247-254, (1992)
[3] Artzner, P.; Delbaen, F.; Eber, J.M.; Heath, D., A characterization of measures of risk, ()
[4] Chateauneuf, A.; Kast, R.; Lapied, A., Choquet pricing for financial markets with frictions, Mathematical finance, 6, 323-330, (1996) · Zbl 0915.90011
[5] Denneberg, D., Preference reversal and the symmetric Choquet integral, ()
[6] Denneberg, D., Non-additive measure and integral, (1994), Kluwer Academic Publishers Boston · Zbl 0826.28002
[7] Dybvig, P.H.; Ross, S.A., Arbitrage, (), 43-50
[8] Hadar, J.; Russell, W., Rules for ordering uncertain prospects, American economic review, 59, 1, 25-34, (1969)
[9] Hickman, J.C.; Young, V.R., Discussion of H.U. gerber and E.S.W. Shiu’s option pricing by esscher transforms, Transactions of the society of actuaries, 46, 99-140, (1994)
[10] Hürlimann, W., Splitting risk and premium calculation, Bulletin of the swiss association of actuaries, 167-197, (1994) · Zbl 0815.62073
[11] Kaas, R.; van Heerwaarden, A.E.; Goovaerts, M.J., Ordering of actuarial risks, () · Zbl 0683.62060
[12] Meyers, G.G., The competitive market equilibrium risk load formula for increased limits ratemaking, (), 163-200
[13] Quiggin, J., Generalized expected utility theory: the rank-dependent model, (1993), Kluwer Academic Publishers Boston
[14] Schmeidler, D., Integral representation without additivity, (), 255-261 · Zbl 0687.28008
[15] Schmeidler, D., Subjective probability and expected utility without additivity, Econometrica, 57, 571-587, (1989) · Zbl 0672.90011
[16] Venter, G.G., Premium calculation implications of reinsurance without arbitrage, ASTIN bulletin, 21, 223-230, (1991)
[17] von Neumann, J.; Morgenstern, O., Theory of games and economic behavior, (1947), Princeton University Press Princeton, NJ · Zbl 1241.91002
[18] Wang, S., Insurance pricing and increased limits ratemaking by proportional hazards transforms, Insurance: mathematics and economics, 17, 43-54, (1995) · Zbl 0837.62088
[19] Wang, S., Premium calculation by transforming the layer premium density, ASTIN bulletin, 26, 71-92, (1996)
[20] Wang, S., Ambiguity-aversion and the economics of insurance, ()
[21] Wang, S.; Young, V.R., Risk-adjusted credibility premiums using distorted probabilities, Scandinavian actuarial journal, (1996), Working paper, submitted to
[22] Yaari, M.E., The dual theory of choice under risk, Econometrica, 55, 95-115, (1987) · Zbl 0616.90005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.