Downside and deviation risk measures are becoming more and more important in many disciplines with clear interfaces with Applied Mathematics and Operations Research. Their dual representations have played critical roles in most of their applications (risk management, portfolio selection, pricing...

We integrate into a single optimization problem a risk measure, beyond the variance, and either arbitrage free real market quotations or financial pricing rules generated by an arbitrage free stochastic pricing model. A sequence of investment strategies such that the couple (expected-return,...