Ordering of risks under PH-transforms. (English) Zbl 0859.90056

Summary: The author recently proposed a premium calculation principle based on proportional hazards (PH) transforms. It is shown that this premium principle resembles the risk-neutral valuation in financial economics, but differs from the traditional utility theory approach. The PH-transform does preserve the stop-loss order of risks which is shared by all risk-averters with increasing concave utility functions.


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


[1] Borch, K.H., The utility concept applied to the theory of insurance, ASTIN bulletin, 1, 170-191, (1961)
[2] Borch, K.H., Optimal insurance arrangements, ASTIN bulletin, 8, 284-290, (1975)
[3] Bühlmann, H., An economic premium principle, ASTIN bulletin, 11, 52-60, (1980)
[4] Bühlmann, H., Premium calculation from top down, ASTIN bulletin, 15, 89-101, (1985)
[5] Cox, J.C.; Ross, S.A., The valuation of options for alternative stochastic processes, Journal of financial economics, 3, 145-166, (1976)
[6] Delbaen, F.; Haezendonck, J., A martingale approach to premium calculation principles in an arbitrage free market, Insurance mathematics and economics, 8, 269-277, (1989) · Zbl 0724.62102
[7] Gerber, H.U.; Shiu, E.S.W., Option pricing by esscher transforms, Transactions of the society of actuaries, XLVI, 99-140, (1994)
[8] Goovaerts, M.J.; de Vylder, F.; Haezendonck, J., Insurance premiums: theory and applications, (1984), North-Holland Amsterdam · Zbl 0532.62082
[9] Goovaerts, M.J.; Kaas, R.; Van Heerwaarden, A.E.; Bauwelinckx, T., ()
[10] Harrison, J.M.; Kreps, D.M., Martingales and arbitrage in multi-period securities markets, Journal of economics theory, 20, 381-408, (1979) · Zbl 0431.90019
[11] Kaas, R.; Van Heerwaarden, A.E., Stop-loss order, unequal means, and more dangerous distributions, Insurance: mathematics and economics, 11, 71-77, (1992) · Zbl 0752.62073
[12] Kaas, R.; Van Heerwaarden, A.E.; Goovaerts, M.J., Ordering of actuarial risks, () · Zbl 0683.62060
[13] Müller, A., Ordering of risks: A comparative study via stop-loss transforms, (), in press · Zbl 0855.62095
[14] Reich, A., Properties of premium calculation principles, Insurance: mathematics and economics, 5, 97-101, (1986) · Zbl 0582.62090
[15] Sondermann, D., Reinsurance in arbitrage-free markets, Insurance: mathematics and economics, 10, 191-202, (1988), (1991) · Zbl 0739.62078
[16] Van Heerwaarden, A.E.; Kaas, R., The Dutch premium principle, Insurance: mathematics and economics, 11, 129-133, (1992) · Zbl 0781.62163
[17] Venter, G.G., Premium calculation implications of reinsurance without arbitrage, ASTIN bulletin, 21, 223-230, (1991)
[18] Wang, S., Insurance pricing and increased limits ratemaking by proportional hazards transforms, Insurance: mathematics and economics, 17, 43-54, (1995) · Zbl 0837.62088
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.