We study bounding approximations for a multistage stochastic program with expected value constraints. Two simpler approximate stochastic programs, which provide upper and lower bounds on the original problem, are obtained by replacing the original stochastic data process by finitely supported approximate processes. We model the original and approximate processes as dependent random vectors on a joint probability space. This probabilistic coupling allows us to transform the optimal solution of the upper bounding problem to a near-optimal decision rule for the original problem. Unlike the scenario tree based solutions of the bounding problems, the resulting decision rule is implementable in all decision stages, i.e., there is no need for dynamic reoptimization during the planning period. Our approach is illustrated with a mean-risk portfolio optimization model.
Credit risk assessment, credit scoring and loan applications approval are one of the typical tasks that can be performed using machine learning or data mining techniques. From this viewpoint, loan applications evaluation is a classification task, in which the final decision can be either a crisp yes/no decision about the loan or a numeric score expressing the financial standing of the applicant. The knowledge to be used is inferred from data about past decisions. These data usually consist off both socio-demographic and economic characteristics of the applicant (e.g., age, income, and deposit), the characteristics of the loan, and the loan approval decision. A number of machine learning algorithms can be used for this purpose. In this paper we show how this task can be performed using the LISp- Miner system, a tool that is under development at the University of Economics, Prague. LISp-Miner is primarily focused on mining for various types of association rules, but unlike "classical" association rules proposed by Agrawal, LISp-Miner in- troduces a greater variety of different types of relations between the left-hand and right-hand sides of a rule. Two other procedures that can be used for classification task are implemented in LISp-Miner as well. We describe the 4ft-Miner and KEX procedures and show how they can be used to analyze data related to loan applications. We also compare the results obtained using the presented algorithms with results from standard rule-learning methods.