Dynamic multistage stochastic optimization programsoffer a possibility to include uncertainty intooptimization models, providing a contemporary set oftools for modern management sciences with wide rangeof applications.In order to solve realistic real-world stochasticoptimization programs, the approximation of theunderlying stochastic process describing the futureuncertainty is performed. In this work, a tree-baseddiscretization technique utilizing conditionaltransportation distance is considered, as it is wellsuited for the approximation of multi-stagestochastic programming problems. Correspondingconvergence properties are investigated. The relationbetweenthe approximation quality of the probability modeland the quality of the solution is established.An example of application, multistage inventorycontrol, is used to verify theoretical results. Thenumerical solution and the obtained error bounds arecalculated explicitly.