Multistage stochastic programs with the entropic risk measure

Over the last two decades, coherent risk measures have been well studied as a principled, axiomatic way to measure the risk of a random variable. Because of this axiomatic approach, coherent risk measures have a number of attractive features for computation, and they have been integrated into a variety of stochastic programming algorithms, including stochastic dual dynamic programming algorithms, a common class of solution methods for multistage stochastic programs. However, even though they facilitate computational tractability, they can suffer from a type of time inconsistency, which we call \textit{conditional inconsistency}. This inconsistency can lead to sub-optimal policies if agents care about their state at the end of the time horizon, but control risk in a stage-wise fashion. The more general class of \textit{convex risk measures} includes the entropic risk measure, which is conditionally consistent and computationally tractable. We explore the relationship between convex risk measures and distributionally robust optimization, and we discuss how to incorporate general convex risk measures into a stochastic dual dynamic programming algorithm.



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