The Expected Shortfall (ES) is one of the most important regulatory risk measures in finance, insurance, and statistics …, which has recently been characterized via sets of axioms from perspectives of portfolio risk management and statistics … the special role of ES in insurance and actuarial science. To fill this gap, we study characterization of risk measures …

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so …-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected … Shortfall (ES), the two popular and competing regulatory risk measures, as special cases. We first establish an inequality for …

We study risk sharing games with quantile-based risk measures and heterogeneous beliefs, motivated by the use of … equivalent to equilibrium allocations, and the equilibrium price is unique. For Value-at-Risk (VaR) agents or mixed VaR and ES … agents, a competitive equilibrium does not exist. Our results generalize existing ones on risk sharing games with risk …