infonet-economy

Coherent risk measures play an important role in building and solving optimization models for decision problems under uncertainty. We consider an extension to multiple time periods, where a risk-adjusted value for a stochastic process is recursively defined over the time steps, which ensures time consistency. A prominent example of a single-period coherent risk measure that is widely used in applications is Conditional-Value-at-Risk (CVaR). We show that a recursive calculation of CVaR leads to stochastic linear programming formulations. For the special case of the risk-adjusted value of a random variable at the time horizon, a lower bound is given. The possible integration of the risk-adjusted value into multi-stage mean-risk optimization problems is outlined.