  This paper studies explicitly solvable multidimensional optimal stopping
problems of sum- and product-type in discrete and continuous time using the
monotone case approach. It gives a review on monotone case stopping using the
Doob decomposition, resp. Doob-Meyer decomposition in continuous time, also in
its multiplicative versions. The approach via these decompositions leads to
explicit solutions for a variety of examples, including multidimensional
versions of the house-selling and burglar's problem, the Poisson disorder
problem, and an optimal investment problem.
