×

A synthesis of risk measures for capital adequacy. (English) Zbl 0951.91032

Summary: We discuss the concept of the risk measure as an expectation using a probability distortion, and classify the standard risk measures according to their associated distortion functions. Using two examples, we explore the features of the different measures.

MSC:

91B30 Risk theory, insurance (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Artzner, P., 1999. Application of coherent risk measures to capital requirements in Finance. North American Actuarial Journal 3 (2). · Zbl 1082.91525
[2] Artzner, P.; Delbaen, F.; Eber, J.-M.; Heath, D., Thinking coherently, Risk, 10, 68-71, (1997)
[3] Artzner, P., Delbaen, F., Eber J.-M., Heath D., 1998. Coherent risk measures. Working paper.
[4] Boyle, P.P.; Hardy, M.R., Reserving for maturity guarantees: two approaches, Insurance: mathematics and economics, 21, 113-127, (1998) · Zbl 0894.90044
[5] Denneberg, D., 1994. Non-additive Measure and Integral. Kluwer Academic Publishers, Dordrecht. · Zbl 0826.28002
[6] Hogg, R.V., Klugman, S.A., 1984. Loss Distributions. Wiley, New York.
[7] Maturity Guarantees Working Party (MGWP), 1980. Journal of the Institute of Actuaries 107, 103-209.
[8] Wang, S.S., Insurance pricing and increased limits ratemaking by proportional hazards transforms, Insurance: mathematics and economics, 17, 43-54, (1995) · Zbl 0837.62088
[9] Wang, S.S., Premium calculation by transforming the layer premium density, ASTIN bulletin, 26, 71-92, (1996)
[10] Wang, S.S., 1997. Implementation of PH transforms in ratemaking. Proceedings of Casualty Actuarial Society.
[11] Wang, S.S., Young, V.R., 1997. Ordering risks: utility theory versus Yaari’s dual theory of risk. Institute of Insurance and Pension Research, University of Waterloo, 97-08
[12] Wang, S.S.; Young, V.R.; Panjer, H.H., Axiomatic characterisation of insurance prices, Insurance: mathematics and economics, 21, 2, 173-183, (1997) · Zbl 0959.62099
[13] Wirch, J.L., 1999. Raising value at risk. North American Actuarial Journal 3 (2). · Zbl 1082.91546
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.