Conditional divergence risk measures

Abstract

Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures. In particular, we study the conditional counterpart of optimized certainty equivalents. In the process, we provide representation results for niveloids in the conditional $L^{\infty }$-space. By employing such representation results we retrieve a conditional version of the variational formula for optimized certainty equivalents. In conclusion, we apply this formula to provide a variational representation of the conditional entropic risk measure.