Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders

Insurance: Mathematics and Economics - Tập 45 Số 3 - Trang 459-465 - 2009
Yongsheng Song1, Jia‐An Yan1
1Center for Financial Engineering and Risk Management, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

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Tài liệu tham khảo

Artzner, 1997, Thinking coherently, Risk, 10, 68

Artzner, 1999, Coherent measures of risk, Mathematical Finance, 9, 203, 10.1111/1467-9965.00068

Cherny, 2007, Dilatation monotone risk measures are law-invariant, Finance and Stochastics, 11, 291, 10.1007/s00780-007-0034-8

Choquet, 1953, Theory of capacity, Ann. Inst. Fourier. (Grenoble), 5, 131, 10.5802/aif.53

Dana, 2005, A representation result for concave Schur concave functions, Mathematical Finance, 15, 615, 10.1111/j.1467-9965.2005.00253.x

Denneberg, 1994

Dhaene, 2006, On the structure of premium principles under pointwise comonotonicity, Theory of Stochastic Processes, 12, 27

Dhaene, 2006, Risk measures and comotononicity: A review, Stochastic Models, 22, 573, 10.1080/15326340600878016

Dhaene, 2000, Comonotonicity and maximal stop-loss premiums, Bulletin of the Swiss Association of Actuaries, 2, 99

Föllmer, 2002, Convex measures of risk and trading constraints, Finance and Stochastics, 6, 429, 10.1007/s007800200072

Föllmer, 2004

Frittelli, 2002, Putting order in risk measures, Journal of Banking Finance, 26, 1473, 10.1016/S0378-4266(02)00270-4

Goovaerts, M., Dhaene, J., 1998. On the characterization of Wang’s class of premium principles. In: Transactions of the 26th International Congress of Actuaries, vol. 4, pp. 121–134

Heyde, C.C., Kou, S.G., Peng, X.H., 2006. What is a good risk measure: Bridging the gaps between data, coherent risk measure, and insurance risk measure. Preprint

Hurlimann, 1998, On stop-loss order and the distorted pricing principle, ASTIN Bulletin, 28, 119, 10.2143/AST.28.1.519082

Jouini, 2006, Law-invariant risk measures have the Fatou property, Advances in Mathematical Economics, 9, 49, 10.1007/4-431-34342-3_4

Kusuoka, 2001, On law-invariant coherent risk measures, Advances in Mathematical Economics, 3, 83, 10.1007/978-4-431-67891-5_4

Laeven, 2005, vol. 360

Meilijson, 1979, Convex majorization with an application to the length of critical paths, Journal of Applied Probability, 16, 671, 10.2307/3213097

Rüschendorf, 1983, Solution of statistical optimization problem by rearrangement methods, Metrika, 30, 55, 10.1007/BF02056901

Schied, 2006, Risk measures and robust optimization problems, Stochastic Models, 22, 753, 10.1080/15326340600878677

Schmeidler, 1989, Subjective probability and expected utility without additivity, Econometrica, 57, 571, 10.2307/1911053

Song, 2006, The representations of two types of functionals on L∞(Ω,F) and L∞(Ω,F,P), Science in China Series A-Mathematics, 49, 1376, 10.1007/s11425-006-2010-8

Wang, 1996, Premium calculation by transforming the layer premium density, ASTIN Bulletin, 26, 71, 10.2143/AST.26.1.563234

Wang, 1998, Comonotonicity, correlation order and premium principles, Insurance: Mathematics and Economics, 22, 235, 10.1016/S0167-6687(97)00040-1

Wang, 1997, Axiomatic characterization of insurance prices, Insurance: Mathematics and Economics, 21, 173, 10.1016/S0167-6687(97)00031-0

Yaari, 1987, The dual theory of choice under risk, Econometrica, 55, 95, 10.2307/1911158