Stochastic Programming of Time-Consistent Extensions of AVaR

We discuss multiperiod stochastic programming formulations of time-consistent extensions of average value-at-risk (AVaR); AVaR measures the risk of a random financial value. Multiperiod risk measures that are recursively defined over time are known to be time consistent. For a multiperiod extension of AVaR for stochastic value processes, we reformulate the recursion as a linear stochastic program, such that the extension can be applied in multiperiod mean-risk optimization. In the special case of risk measurement for a final random value at a time horizon, we give a lower bound in terms of AVaR.