We consider the problem of optimal portfolio choice using the lower partial moments
risk measure for a market consisting of n risky assets and a riskless asset. For when the
mean return vector and variance/covariance matrix of the risky assets are specified without
specifying a return distribution, we derive distributionally robust portfolio rules. We then
address potential uncertainty (ambiguity) in the mean return vector as well, in addition to
distribution ambiguity, and derive a closed-form portfolio rule for when the uncertainty in
the return vector is modelled via an ellipsoidal uncertainty set. Our result also indicates a
choice criterion for the radius of ambiguity of the ellipsoid. Using the adjustable robustness
paradigm we extend the single-period results to multiple periods, and derive closed-form
dynamic portfolio policies which mimic closely the single-period policy.
