Risk-Management Models Based on the Portfolio Theory Using Historical Data under Uncertainty

A mission in this chapter is to extend previous mathematical programming problems using historical data to stochastic and fuzzy programming problems under uncertainty, particularly considering the risk-management. In the practice decision making, it is necessary to take various constraints and assumptions into consideration as well as uncertainty, such as the probability derived from the statistical analysis of historical data and the ambiguity derived from lack of reliable information and decision maker’s subjectivity. Since it is difficult that decision makers know precise information due to such uncertainty, they need to make appropriate decisions under uncertainty. Until now, in order to deal with uncertainty in the sense of mathematical programming, many studies with respect to stochastic and fuzzy programming have been performed. Stochastic programming is ABSTRACT