Risk aggregation with dependence uncertainty

Albrecher, 2008, General lower bounds for arithmetic Asian option prices, Appl. Math. Finance, 15, 123, 10.1080/13527260701356633

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

Basel Committee on Banking Supervision 2010. Developments in Modelling Risk Aggregation. Basel: Bank for International Settlements.

Basel Committee on Banking Supervision 2012. Consultative Document May 2012. Fundamental Review of the Trading Book. Basel: Bank for International Settlements.

Bäuerle, 2006, Stochastic orders and risk measures: consistency and bounds, Insurance Math. Econom., 38, 132, 10.1016/j.insmatheco.2005.08.003

Bernard, 2012, Note on improved Fréchet bounds, J. Appl. Probab., 49, 866, 10.1239/jap/1346955339

Bernard, 2013, Bounds on capital requirements for bivariate risk with given marginals and partial information on the dependence, Dependence Model., 1, 37

Bernard, C., Rüschendorf, L., Vanduffel, S., 2013b. Value-at-risk bounds with variance constraints. Working Paper. Available at SSRN:http://ssrn.com/abstract=2342068.

Cheung, 2013, Bounds for sums of random variables when the marginal distributions and the variance of the sum are given, Scand. Actuar. J., 2, 103, 10.1080/03461238.2011.558186

Cont, 2006, Model uncertainty and its impact on the pricing of derivative instruments, Math. Finance, 16, 519, 10.1111/j.1467-9965.2006.00281.x

D’Aspremont, 2006, Static arbitrage bounds on basket option prices, Math. Program. Ser. A and B, 106, 467, 10.1007/s10107-005-0642-z

Delbaen, 2002, Coherent measures of risk on general probability spaces, 1

Delbaen, 2009, Risk measures for non-integrable random variables, Math. Finance, 19, 329, 10.1111/j.1467-9965.2009.00370.x

Denuit, 1999, Stochastic bounds on sums of dependent risks, Insurance Math. Econom., 25, 85, 10.1016/S0167-6687(99)00027-X

Dhaene, 2002, The concept of comonotonicity in actuarial science and finance: theory, Insurance Math. Econom., 31, 3, 10.1016/S0167-6687(02)00134-8

Dhaene, 2012, The herd behavior index: a new measure for the implied degree of co-movement in stock markets, Insurance Math. Econom., 50, 357, 10.1016/j.insmatheco.2012.01.005

Dhaene, 2006, Risk measures and comonotonicity: a review, Stoch. Models, 22, 573, 10.1080/15326340600878016

Embrechts, 2003, Using copulae to bound the value-at-risk for functions of dependent risks, Finance Stoch., 7, 145, 10.1007/s007800200085

Embrechts, 2006, Bounds for functions of dependent risks, Finance Stoch., 10, 341, 10.1007/s00780-006-0005-5

Embrechts, 2010, Risk aggregation, vol. 198

Embrechts, 2013, Model uncertainty and VaR aggregation, J. Banking Finance, 37, 2750, 10.1016/j.jbankfin.2013.03.014

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

Föllmer, 2010, Coherent and convex risk measures, 355

Hobson, 2005, Static-arbitrage upper and lower bounds for the prices of basket options, Quant. Finance, 5, 329, 10.1080/14697680500151392

Kaas, 2000, Upper and lower bounds for sums of random variables, Insurance Math. Econom., 27, 151, 10.1016/S0167-6687(00)00060-3

Kaas, 2009, Worst VaR scenarios with given marginals and measures of association, Insurance Math. Econom., 44, 146, 10.1016/j.insmatheco.2008.12.004

Kaina, 2009, On convex risk measures on Lp-spaces, Math. Methods Oper. Res., 69, 475, 10.1007/s00186-008-0248-3

Keller-Ressel, M., Clauss, G., 2012. Convex order of discrete, continuous and predictable quadratic variation & applications to options on variance. Working Paper. Available on ArXiv.

Kusuoka, 2001, On law invariant coherent risk measures, Adv. Math. Econ., 3, 83, 10.1007/978-4-431-67891-5_4

McNeil, 2005

Meilijson, 1979, Convex majorization with an application to the length of critical paths, J. Appl. Probab., 16, 671, 10.2307/3213097

Müller, 1997, Stop-loss order for portfolios of dependent risks, Insurance Math. Econom., 21, 219, 10.1016/S0167-6687(97)00032-2

Müller, 1997, Stochastic orderings generated by integrals: a unified study, Adv. Appl. Probab., 29, 414, 10.2307/1428010

Panjer, 2006

Puccetti, 2013, Sharp bounds on the expected shortfall for a sum of dependent random variables, Statist. Probab. Lett., 83, 1227, 10.1016/j.spl.2013.01.022

Puccetti, 2012, Computation of sharp bounds on the distribution of a function of dependent risks, J. Comput. Appl. Math., 236, 1833, 10.1016/j.cam.2011.10.015

Puccetti, 2012, Advances in complete mixability, J. Appl. Probab., 49, 430, 10.1239/jap/1339878796

Rogers, 1995, The value of an Asian option, J. Appl. Probab., 32, 1077, 10.2307/3215221

Rüschendorf, 1980, Inequalities for the expectation of Δ-monotone functions, Z. Wahrscheinlichkeitstheor., 54, 341, 10.1007/BF00534351

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

Svindland, G., 2008. Convex Risk Measures Beyond Bounded Risk. Ph.D. Thesis, Ludwig Maximilian Universität München.

Tankov, 2011, Improved Fréchet bounds and model-free pricing of multi-asset options, J. Appl. Probab., 48, 389, 10.1239/jap/1308662634

Tchen, 1980, Inequalities for distributions with given marginals, Ann. Probab., 8, 814, 10.1214/aop/1176994668

Valdez, 2009, Bounds and approximations for sums of dependent log-elliptical random variables, Insurance Math. Econom., 44, 385, 10.1016/j.insmatheco.2008.11.007

Wang, 2013, Bounds for the sum of dependent risks and worst value-at-risk with monotone marginal densities, Finance Stoch., 17, 395, 10.1007/s00780-012-0200-5

Wang, 2011, The complete mixability and convex minimization problems for monotone marginal distributions, J. Multivariate Anal., 102, 1344, 10.1016/j.jmva.2011.05.002