Dynamic multistage stochastic optimization programs offer a possibility to include uncertainty into optimization models, providing a contemporary set of tools for modern management sciences with wide range of applications. In order to solve realistic real-world stochastic optimization programs, the approximation of the underlying stochastic process describing the future uncertainty is performed. In this work, a tree-based discretization technique utilizing conditional transportation distance is considered, as it is well suited for the approximation of multi-stage stochastic programming problems. Corresponding convergence properties are investigated. The relation between the approximation quality of the probability model and the quality of the solution is established. An example of application, multistage inventory control, is used to verify theoretical results. The numerical solution and the obtained error bounds are calculated explicitly.

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