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** (.):** optimal stopping problem, Snells envelope, stopping region

**:** . , Maple 14, .

** (.):** We propose an algorithm that solves the optimal stopping problem with the finite horizon. The algorithm is based on a derived recurrent equation for the optimal stopping time. It fulfils "separation" principle of solving the optimal stopping problem. This algorithm, implemented in Maple 14 system of computer algebras, is used to solve optimal stopping problems for several discrete Markovian sequences.

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