Improved Hoeffding–Fréchet bounds and applications to VaR estimates

[1]  Ruodu Wang,et al.  Risk bounds for factor models , 2017, Finance Stochastics.

[2]  Ludger Rüschendorf,et al.  Risk Bounds and Partial Dependence Information , 2017 .

[3]  L. Rüschendorf,et al.  VaR bounds for joint portfolios with dependence constraints , 2016 .

[4]  A. Papapantoleon,et al.  Improved Fr\'echet--Hoeffding bounds on $d$-copulas and applications in model-free finance , 2016, 1602.08894.

[5]  Ludger Rüschendorf,et al.  How robust is the value-at-risk of credit risk portfolios? , 2015 .

[6]  Ludger Rüschendorf,et al.  Reduction of Value-at-Risk bounds via independence and variance information , 2015 .

[7]  C. Sempi,et al.  Principles of Copula Theory , 2015 .

[8]  Ruodu Wang,et al.  Extremal Dependence Concepts , 2015, 1512.03232.

[9]  S. Vanduffel,et al.  A New Approach to Assessing Model Risk in High Dimensions , 2015 .

[10]  Ludger Rüschendorf,et al.  Value-at-Risk Bounds with Variance Constraints , 2015 .

[11]  Ludger Rüschendorf,et al.  Reducing Model Risk via Positive and Negative Dependence Assumptions , 2015 .

[12]  P. Embrechts,et al.  An Academic Response to Basel 3.5 , 2014 .

[13]  Ruodu Wang,et al.  Complete mixability and asymptotic equivalence of worst-possible VaR and ES estimates , 2013 .

[14]  P. Embrechts,et al.  Model Uncertainty and VaR Aggregation , 2013 .

[15]  Z. Shishebor,et al.  Sharp Bounds on a Class of Copulas with known Values at Several Points , 2013 .

[16]  Ludger Rüschendorf,et al.  Mathematical Risk Analysis: Dependence, Risk Bounds, Optimal Allocations and Portfolios , 2013 .

[17]  Ludger Rüschendorf,et al.  Sharp Bounds for Sums of Dependent Risks , 2013, J. Appl. Probab..

[18]  Beatrice Acciaio,et al.  A MODEL‐FREE VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING AND THE SUPER‐REPLICATION THEOREM , 2013, 1301.5568.

[19]  C. Bernard,et al.  Bounds on Capital Requirements For Bivariate Risk with Given Marginals and Partial Information on the Dependence , 2013 .

[20]  Mathias Beiglböck,et al.  Model-independent bounds for option prices—a mass transport approach , 2011, Finance Stochastics.

[21]  Ludger Rüschendorf,et al.  Bounds for joint portfolios of dependent risks , 2012 .

[22]  Carole Bernard,et al.  A Note on 'Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options' by Tankov (2011) , 2012, J. Appl. Probab..

[23]  R W,et al.  Bounds for the Sum of Dependent Risks and Worst Value-at-Risk with Monotone Marginal Densities , 2012 .

[24]  Bin Wang,et al.  The complete mixability and convex minimization problems with monotone marginal densities , 2011, J. Multivar. Anal..

[25]  Huimei Liu,et al.  Best possible upper bound on VaR for dependent portfolio risk , 2011 .

[26]  Peter Tankov,et al.  Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options , 2011, Journal of Applied Probability.

[27]  Paul Embrechts,et al.  Bounds for the sum of dependent risks having overlapping marginals , 2010, J. Multivar. Anal..

[28]  Paul Embrechts,et al.  Aggregating risk capital, with an application to operational risk , 2006 .

[29]  Paul Embrechts,et al.  Bounds for Functions of Dependent Risks , 2006, Finance Stochastics.

[30]  Ludger Rüschendorf,et al.  Monge – Kantorovich transportation problem and optimal couplings , 2006 .

[31]  Jean-François Quessy,et al.  Bounds on the value-at-risk for the sum of possibly dependent risks , 2005 .

[32]  Ludger R√ºschendorf,et al.  Stochastic Ordering of Risks, Influence of Dependence, and A.S. Constructions , 2005 .

[33]  Manuel Úbeda-Flores,et al.  Best-Possible Bounds on Sets of Multivariate Distribution Functions , 2005 .

[34]  Roger B. Nelsen,et al.  Best-possible bounds on sets of bivariate distribution functions , 2004 .

[35]  L. Rüschendorf Comparison of multivariate risks and positive dependence , 2004, Journal of Applied Probability.

[36]  Paul Embrechts,et al.  Using copulae to bound the Value-at-Risk for functions of dependent risks , 2003, Finance Stochastics.

[37]  Assignment Models for Constrained Marginals and Restricted Markets , 2002 .

[38]  C. Genest,et al.  Stochastic bounds on sums of dependent risks , 1999 .

[39]  S. Rachev,et al.  Mass transportation problems , 1998 .

[40]  Duality Theorems for Assignments with upper Bounds , 1997 .

[41]  Svetlozar T. Rachev,et al.  Solution of Some Transportation Problems with Relaxed or Additional Constraints , 1994 .

[42]  L. Rüschendorf Bounds for distributions with multivariate marginals , 1991 .

[43]  L. Rüschendorf FréChet-Bounds and Their Applications , 1991 .

[44]  Robert C. Williamson,et al.  Probabilistic arithmetic. I. Numerical methods for calculating convolutions and dependency bounds , 1990, Int. J. Approx. Reason..

[45]  M. J. Frank,et al.  Best-possible bounds for the distribution of a sum — a problem of Kolmogorov , 1987 .

[46]  H. Kellerer Duality theorems for marginal problems , 1984 .

[47]  Ludger Rüschendorf,et al.  Solution of a statistical optimization problem by rearrangement methods , 1983 .

[48]  K. Worsley An improved Bonferroni inequality and applications , 1982 .

[49]  G. D. Makarov Estimates for the Distribution Function of a Sum of Two Random Variables When the Marginal Distributions are Fixed , 1982 .

[50]  Stochastic Inequalities,et al.  RANDOM VARIABLES WITH MAXIMUM SUMS , 1982 .

[51]  L. Rüschendorf Sharpness of Fréchet-bounds , 1981 .

[52]  N. Gaffke,et al.  On a class of extremal problems in statistics , 1981 .

[53]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[54]  Ludger Rüschendorf,et al.  Inequalities for the expectation of Δ-monotone functions , 1980 .

[55]  A. Nádas,et al.  Convex majorization with an application to the length of critical paths , 1979, Journal of Applied Probability.

[56]  G. Simons,et al.  Inequalities for Ek(X, Y) when the marginals are fixed , 1976 .

[57]  David J. Hunter An upper bound for the probability of a union , 1976, Journal of Applied Probability.

[58]  A. Tchen Inequalities for distributions with given marginals , 1976 .

[59]  E. Kounias Bounds for the Probability of a Union, with Applications , 1968 .

[60]  George G. Lorentz,et al.  An Inequality for Rearrangements , 1953 .