Quasiconvex risk statistics with scenario analysis

详细信息    查看全文

• 作者：Dejian Tian (1)
  Long Jiang (1)
  
  1. School of Sciences ; China University of Mining and Technology ; Xuzhou ; 221116 ; China
  
• 关键词：Quasiconvex risk statistics ; Empirical ; law ; invariance ; Scenario analysis ; Comonotonic quasiconvexity ; G10 ; C65
• 刊名：Mathematics and Financial Economics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：9
• 期：2
• 页码：111-121
• 全文大小：174 KB
• 参考文献：1. Ahmed, S, Filipovic, D, Svindland, G (2008) A note on natural risk statistics. Oper. Res. Lett. 36: pp. 662-664 CrossRef
  2. Artzner, P, Delbaen, F, Eber, JM, Heath, D (1999) Coherent measures of risk. Math. Financ. 4: pp. 203-228 CrossRef
  3. Assa, H, Morales, M (2010) Risk measures on the space of infinite sequences. Math. Financ. Econ. 2: pp. 253-275 CrossRef
  4. Basel Committee on Banking Supervision. Revisions to the Basel II Market Risk Framework. February (2011)
  5. Cerreia-Vioglio, S, Maccheroni, F, Marinacci, M, Montrucchio, L (2011) Risk measures: rationality and diversification. Math. Financ. 21: pp. 743-774
  6. Dana, RA (2005) A representation result for concave Schur concave functions. Math. Financ. 14: pp. 613-634 CrossRef
  7. F枚llmer, H, Schied, A (2002) Convex measures of risk and trading constraints. Financ. Stoch. 6: pp. 429-447 CrossRef
  8. Frittelli, M, Maggis, M (2011) Dual representation of quasi-convex conditional maps. SIAM J. Financ. Math. 2: pp. 357-382 CrossRef
  9. Frittelli, M, Rosazza Gianin, E (2002) Putting order in risk measures. J. Bank. Financ. 26: pp. 1473-1486 CrossRef
  10. Frittelli, M, Rosazza Gianin, E (2005) Law invariant convex risk measures. Adv. Math. Econ. 7: pp. 33-46 CrossRef
  11. Frittelli, M, Rosazza Gianin, E (2011) On the penalty function and on continuity properties of risk measures. Int. J. Theor. Appl. Financ. 14: pp. 163-185 CrossRef
  12. Heyde, C.C., Kou, S.G., Peng, X.H.: What is a good external risk measure: Bridging the gaps between robustness, subadditivity, and insurance risk measures, Preprint (2007)
  13. Kou, SG, Peng, XH, Heyde, CC (2013) External risk measures and basel accords. Math. Oper. Res. 38: pp. 393-417 CrossRef
  14. Kusuoka, S (2001) On law invariant coherent risk measures. Adv. Math. Econ. 3: pp. 83-95 CrossRef
  15. Leitner, J (2005) A short note on second-order stochastic dominance preserving coherent risk measures. Math. Financ. 15: pp. 649-651 CrossRef
  16. Song, Y, Yan, J (2006) The representations of two types of functionals on $$L^{\infty }(\Omega , {\cal F})$$ L 鈭( 惟 , F ) and $$L^{\infty }(\Omega ,{\cal F},P)$$ L 鈭( 惟 , F , P ). Sci. China Ser. A: Math. 49: pp. 1376-1382 CrossRef
  17. Song, Y, Yan, J (2009) Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders. Insur.: Math. Econ. 45: pp. 459-465
  18. Tian, D, Suo, X (2012) A note on convex risk statistic. Oper. Res. Lett. 40: pp. 551-553 CrossRef
  19. Volle, M (1998) Duality for the level sum of quasiconvex functions and applications. ESAIM Control Optim. Calc. Var. 3: pp. 329-343 CrossRef
  20. Wang, SS, Young, VR, Panjer, HH (1997) Axiomatic characterization of insurance prices. Insur.: Math. Econ. 21: pp. 173-183
  21. Xia, J.: Comonotomic convex preferences, working paper (2013)
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Quantitative Finance
  Finance and Banking
  Financial Economics
  Game Theory and Mathematical Methods
  Applications of Mathematics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1862-9660

文摘

We introduce the definitions of quasiconvex risk statistics. Using dual method, we provide representation results for comonotonic quasiconvex risk statistics and empirical-law-invariant quasiconvex risk statistics. In particular, we present some specific examples related to certainty equivalence and Basel margin requirement.