Risk measures with comonotonic subadditivity or convexity on product spaces

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• 作者：Lin-xiao Wei ; Yue Ma ; Yi-jun Hu
• 关键词：91B30 ; 91B32 ; 91B70 ; Choquet integral ; comonotonic subadditivity risk measure ; comonotonic convex risk measure ; multi ; period risk measure ; capital allocation ; product space
• 刊名：Applied Mathematics - A Journal of Chinese Universities
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：30
• 期：4
• 页码：407-417
• 全文大小：196 KB
• 参考文献：[1]P Artzner, F Delbaen, J M Eber, D Heath. Thinking coherently, Risk, 1997, 10: 68鈥?1.
  [2]P Artzner, F Delbaen, J M Eber, D Heath. Coherent measures of risk, Math Finance, 1999, 9(3): 203鈥?28.CrossRef MathSciNet
  [3]C Burgert, L R眉schendorf. Consistent risk measures for portfolio vectors, Insurance Math Econom, 2006, 38: 289鈥?97.CrossRef MathSciNet
  [4]A Balb谩s, R Balb谩s, P Jim茅nez-Guetta. Vector risk functions, Mediterr J Math, 2012, 9: 563鈥?74.CrossRef MathSciNet
  [5]I Cascos, I Molchanov. Multivariate risks and depth-trimmed regions, Finance Stoch, 2007, 11: 373鈥?97.CrossRef MathSciNet
  [6]F Delbaen. Coherent risk measures on general probability spaces, In: Advances in Finance and Stoshatics, Springer, 2002: 1鈥?7.CrossRef
  [7]M Denault. Coherent allocation of risk capital, J Risk, 2001, 4(1): 7鈥?1.
  [8]D Denneberg. Non-additive measure and integral, Kluwer Academic Publishers, 1994.CrossRef
  [9]O Deprez, U Gerber, Hans. On convex principles of premium calculation, Insurance Math Econom, 1985, 4(3): 179鈥?89.CrossRef MathSciNet
  [10]P Embrechts, G Puccetti. Bounds for functions of multivariate risks, J Multivariate Anal, 2006, 97: 526鈥?47.CrossRef MathSciNet
  [11]H F枚llmer, A Schied. Convex measures of risk and trading constraints, Finance Stoch, 2002, 6: 429鈥?47.CrossRef MathSciNet
  [12]H F枚llmer, A Schied. Stochastic Finance: An Introduction in Discrete Time, Walter de Gruyter, 2011.
  [13]M Frittelli, E Rosazza Gianin. Putting order in risk measures, J Bank Financ, 2002, 26 1473鈥?486.
  [14]M Frittelli, G Scandolo. Risk measures and capital requirements for processes, Math Finance, 2006, 16(4): 589鈥?12.CrossRef MathSciNet
  [15]A H Hamel. Translative sets and functions and their applications to risk measure theory and nonlinear separation, IMPA, Preprint D 21/2006.
  [16]A Hamel, F Heyde. Duality for set-valued measures of risk, SIAM J Financ Math, 2010, 1: 66鈥?5.CrossRef MathSciNet
  [17]W Jouini, M Meddeb, N Touzi. Vector-valued coheret risk measures, Finance Stoch, 2004, 8: 531鈥?52.MathSciNet
  [18]A V Kulikov. Multidimensional coherent and convex risk measures, Theory Probab Appl, 2008, 52(4): 614鈥?35.CrossRef MathSciNet
  [19]L R眉schendorf. Mathematical Risk Analysis, Springer, 2013.CrossRef
  [20]Y Song, J Yan. The representation of two types of functionals on L 鈭?/sup> (惟,F) and L 鈭?/sup> (惟,F, P), Sci China Ser A, 2006, 49(10): 1376鈥?382.CrossRef MathSciNet
  [21]Y Song, J Yan. Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders, Insurance Math Econom, 2009, 45: 459鈥?65.CrossRef MathSciNet
  [22]L Wei, Y Hu. Coherent and convex risk measures for portfolios with applications, Statist Probab Lett, 2014, 90: 114鈥?20.CrossRef MathSciNet
  [23]J Yan. An Introduction to the Financial Mathematics, Chinese Academic Press, Beijing, 2012.
  [24]J Yan. A short presentation of Choquet integral, In: Recent Development in Stochastic Dynamics & Stochastic Analysis, Interdiscip Math Sci, 2009, 8: 269鈥?91.
  
• 作者单位：Lin-xiao Wei (1)
  Yue Ma (1)
  Yi-jun Hu (1)
  
  1. College of Science, Wuhan University of Technology, Wuhan, 430070, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Applications of Mathematics
  Chinese Library of Science
  
• 出版者：Editorial Committee of Applied Mathematics - A Journal of Chinese Universities
• ISSN：1993-0445

文摘

In this paper, by an axiomatic approach, we propose the concepts of comonotonic subadditivity and comonotonic convex risk measures for portfolios, which are extensions of the ones introduced by Song and Yan (2006). Representation results for these new introduced risk measures for portfolios are given in terms of Choquet integrals. Links of these newly introduced risk measures to multi-period comonotonic risk measures are represented. Finally, applications of the newly introduced comonotonic coherent risk measures to capital allocations are provided. Keywords Choquet integral comonotonic subadditivity risk measure comonotonic convex risk measure multi-period risk measure capital allocation product space