This book provides the first systematic treatment of model risk, outlining the tools needed to quantify model uncertainty, to study its effects and, in particular, to determine best upper and lower risk bounds for various risk aggregation functionals of interest. Drawing on both numerical and analytical examples, this is a thorough reference for actuaries, risk managers, and regulators. Supervisory authorities can use the methods discussed to challenge the models used by banks and insurers, and banks and insurers can use them to prioritize the activities on model development: which ones require more attention than others? In sum, it is essential reading for all those working in portfolio theory and the theory of financial and engineering risk, for practitioners in these areas, and can also be used with graduate courses on risk bounds and model uncertainty.