Two Algorithms for Risk-averse Reformulation of Multi-stage Stochastic Programming Problems

Many real-life applications lead to risk-averse multi-stage stochastic problems; therefore effective solution of these problems is of great importance. Many tools can be used to their solution (GAMS, Coin-OR, APML or, for smaller problems, Excel); it is, however, mostly up to researcher to reformulate the problem into its deterministic equivalent. Moreover, such solutions are usually one-time, not easy to modify for different applications. We overcome these problems by providing a front-end software package, written in C++, which enables to enter problem definitions in a way close to their mathematical definition. Creating of a deterministic equivalent (and its solution) is up to the computer. In particular, our code is able to solve linear multi-stage with Multi-period Mean-CVaR or Nested Mean-CVaR criteria. In the present paper, we describe the algorithms, transforming these problems into their deterministic equivalents.