sentences:  When the underlying process (or the gain process) is described by its unconditional finite-dimensional distributions, the appropriate solution technique is the martingale approach, so called because it uses martingale theory, the most important concept being the Snell envelope.In the discrete time case, if the planning horizon formula_13 is finite, the problem can also be easily solved by dynamic programming.When the underlying process is determined by a family of (conditional) transition functions leading to a Markov family of transition probabilities, powerful analytical tools provided by the theory of Markov processes can often be utilized and this approach is referred to as the Markov method.