Mean? portfolio selection and ?arbitrage for coherent risk measures

We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by positively homogeneous measure . first show that under mild assumptions, the set of optimal portfolios for fixed return nonempty and compact. However, unlike classical mean-variance selection, it can happen no efficient exist. call this situation -arbitrage, prove cannot be excluded—unless as conservative worst-case measure. After providing primal characterization we focus our attention on coherent measures admit dual representation give necessary sufficient -arbitrage. absence -arbitrage intimately linked to interplay between equivalent martingale (EMMs) discounted risky assets absolutely continuous A special case result shows does not Expected Shortfall at level if only there exists an EMM such