Before revision:  For the case where the consistent measures are given by Average Value-at-Risk, we derive a polynomial-time algorithm for approximating an arbitrary inconsistent distortion measure. We also present exact analytical bounds for the case where the dynamically inconsistent measureis also given by Average Value-at-Risk, and briefly discuss managerial implications in multi-period risk-assessment processes  .
After revision:  For the case where the consistent measures are given by Average Value-at-Risk, we derive a polynomial-time algorithms are possible. One such case is the well-known Conditional Value-at-Risk measure, which is further explored in our companion paper .