We consider the evaluation of financial derivatives with American features using local and global hedging strategies. In addition to the quadratic risk measure, our exploration involves the use and comparison of alternative models based on the conditional value-at-risk. In opposition to local risk minimization strategies, the proposed approaches use global hedging strategies based on mixes of risk measures and state-dynamic equations that control the overall risk. They are solved using backward stochastic dynamic programming that we imbed with parametric technics to speed up the running time and cope with the curse of dimensionality in dynamic programming. To demonstrate the flexibility of our strategies, we present numerical examples featuring American put options.