The bounds for risk measures of a portfolio when its components have known marginal distributions but the dependence among the risks is unknown are often too wide to be useful in practice. Moreover, availability of additional dependence information, such as knowledge of some higher-order...

We investigate the impact of counterparty risk on contract design in the reinsurance market. We study a multiplicative default risk model, with partial recovery and where the probability of the reinsurer's default depends on the loss incurred by the insurer. The seller is assumed to be...

Nelsen et al. (2004) find bounds for bivariate distribution functions when there are constraints on the values of its quartiles. Tankov (2011) generalizes this work by giving explicit expressions for the best upper and lower bounds for a bivariate copula when its values on a compact subset of...

We study the impact of dependence uncertainty on E(X_1X_2 · · · X_d) when X_i ∼ F_i for all i. Under some conditions on the Fi, explicit sharp bounds are obtained and a numerical method is provided to approximate them for arbitrary choices of the F_i. The results are applied to assess the...