  Previous literature shows that prevalent risk measures such as Value at Risk
or Expected Shortfall are ineffective to curb excessive risk-taking by a
tail-risk-seeking trader with S-shaped utility function in the context of
portfolio optimisation. However, these conclusions hold only when the
constraints are static in the sense that the risk measure is just applied to
the terminal portfolio value. In this paper, we consider a portfolio
optimisation problem featuring S-shaped utility and a dynamic risk constraint
which is imposed throughout the entire trading horizon. Provided that the risk
control policy is sufficiently strict relative to the asset performance, the
trader's portfolio strategies and the resulting maximal expected utility can be
effectively constrained by a dynamic risk measure. Finally, we argue that
dynamic risk constraints might still be ineffective if the trader has access to
a derivatives market.
