  We study mean-risk optimal portfolio problems where risk is measured by
Recovery Average Value at Risk, a prominent example in the class of recovery
risk measures. We establish existence results in the situation where the joint
distribution of portfolio assets is known as well as in the situation where it
is uncertain and only assumed to belong to a set of mixtures of benchmark
distributions (mixture uncertainty) or to a cloud around a benchmark
distribution (box uncertainty). The comparison with the classical Average Value
at Risk shows that portfolio selection under its recovery version enables
financial institutions to exert better control on the recovery on liabilities
while still allowing for tractable computations.
