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Finan. Math."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We incorporate a notion of risk aversion favoring prudent decisions from financial institutions into regulatory capital calculation principles. In the context of Basel III and IV as well as Solvency II, regulatory capital calculation is carried out through the tools of monetary risk measures. The notion of risk aversion that we focus on has four equivalent formulations: through consistency with second-order stochastic dominance, conditional expectations, or portfolio diversification, and through expected social impact. The class of monetary risk measures representing this notion of risk aversion is referred to as consistent risk measures. We characterize the class of consistent risk measures by establishing an Expected Shortfall (ES)-based representation, and as a by-product, we obtain new results on the representation of convex risk measures. We present several examples where consistent risk measures naturally appear. Using the obtained representation results, we study risk sharing and optimal investment problems and find several new analytical solutions.<\/jats:p>","DOI":"10.1137\/18m121842x","type":"journal-article","created":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T15:22:11Z","timestamp":1584026531000},"page":"169-200","source":"Crossref","is-referenced-by-count":39,"title":["Risk Aversion in Regulatory Capital Principles"],"prefix":"10.1137","volume":"11","author":[{"given":"Tiantian","family":"Mao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruodu","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,3,12]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfs.2009.02.001"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00068"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-005-0152-0"},{"key":"atypb4","unstructured":"BCBS (2016),\n                      Standards. 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Wang (2018),\n                      Robustness in the Optimization of Risk Measures\n                      , SSRN research paper 3254587,https:\/\/ssrn.com\/abstract=3254587.","DOI":"10.2139\/ssrn.3254587"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2009.00380.x"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/s00780-008-0069-5"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2012.00534.x"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1214\/16-AOS1439"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1007\/s007800200072"},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":"H. F\u00f6llmer and A. Schied (2011),\n                      Stochastic Finance: An Introduction in Discrete Time\n                      , 3rd ed., Walter de Gruyter, Berlin.","DOI":"10.1515\/9783110218053"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4266(02)00270-4"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/4-431-27233-X_2"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2010.00432.x"},{"key":"atypb26","unstructured":"IAIS (2014),\n                      Consultation Document: Risk-Based Global Insurance Capital Standard\n                      , International Association of Insurance Supervisors, Basel, Switzerland."},{"key":"atypb27","doi-asserted-by":"crossref","unstructured":"J. Jia and J. S. 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Embrechts (2015),\n                      Quantitative Risk Management: Concepts, Techniques and Tools\n                      , rev. ed., Princeton University Press, Princeton, NJ."},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1287\/moor.26.4.723.10006"},{"key":"atypb38","doi-asserted-by":"crossref","unstructured":"A. M\u00fcller, M. Scarsini, I. Tsetlin, and R. L. Winkler (2017),\n                      Between first- and second-order stochastic dominance\n                      , Management Sci., 63, pp. 2933-2947.","DOI":"10.1287\/mnsc.2016.2486"},{"key":"atypb39","unstructured":"A. M\u00fcller and D. Stoyan (2002),\n                      Comparison Methods for Stochastic Models and Risks\n                      , John Wiley & Sons, Ltd., Chichester, UK."},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1214\/15-STS525"},{"key":"atypb41","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(70)90038-4"},{"key":"atypb42","doi-asserted-by":"crossref","unstructured":"L. R\u00fcschendorf (2013),\n                      Mathematical Risk Analysis. Dependence, Risk Bounds, Optimal Allocations and Portfolios\n                      , Springer, Heidelberg.","DOI":"10.1007\/978-3-642-33590-7"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1214\/105051604000000341"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1016\/S1570-8659(08)00002-1"},{"key":"atypb45","doi-asserted-by":"crossref","unstructured":"M. Shaked and J. G. Shanthikumar (2007),\n                      Stochastic Orders\n                      , Springer Ser. 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