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Economic capital allocation derived from risk measures. (English) Zbl 1084.91515

Summary: We examine properties of risk measures that can be considered to be in line with some ’best practice’ rules in insurance, based on solvency margins. We give ample motivation that all economic aspects related to an insurance portfolio should be considered in the definition of a risk measure. As a consequence, conditions arise for comparison as well as for addition of risk measures. We demonstrate that imposing properties that are generally valid for risk measures, in all possible dependency structures, based on the difference of the risk and the solvency margin, though providing opportunities to derive nice mathematical results, violate best practice rules. We show that so-called coherent risk measures lead to problems. In particular we consider an exponential risk measure related to a discrete ruin model, depending on the initial surplus, the desired ruin probability and the risk distribution.

MSC:

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

[1] Artzner P., North American Actuarial Journal 3 (2) pp 11– (1999) · Zbl 1082.91525
[2] Artzner P., Mathematical Finance 9 pp 203– (1999) · Zbl 0980.91042
[3] Bühlmann H., ASTIN Bulletin 15 pp 89– (1985)
[4] Dhaene J., Insurance: Mathematics and Economics 31 (1) pp 31– (2002)
[5] Dhaene J., Insurance: Mathematics and Economics 31 (2) pp 133– (2002) · Zbl 1037.62107
[6] Gerber H. U., An Introduction to Mathematical Risk Theory (1979) · Zbl 0431.62066
[7] Goovaerts M. J., Insurance Premiums (1984) · Zbl 0532.62082
[8] Goovaerts M. J., Tijdschrift voor Economie en Management 44 (4) pp 545– (2001)
[9] Kaas R., Modern Actuarial Risk Theory (2001) · Zbl 1086.91035
[10] Panjer H. H., Research Report 01-15 (2001)
[11] Rothschild M., Journal of Economic Theory 2 pp 225– (1970)
[12] Rothschild M., Journal of Economic Theory 3 pp 66– (1971)
[13] Shiu E. S. W., North American Actuarial Journal 4 (1) pp 115– (2000) · Zbl 1083.91553
[14] Wang S., ASTIN Bulletin 26 pp 71– (1996)
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