Investment models based on clustered scenario trees

Stochastic programming is widely applied in financial decision problems. In particular, when we need to carry out the actual calculations for portfolio selection problems, we have to assign a value for each expected return and the associated conditional probability in advance. These estimated random parameters often rely on a scenario tree representing the distribution of the underlying asset returns. One of the drawbacks is that the estimated parameters may be deviated from the actual ones. Therefore, robustness is considered so as to cope with the issue of parameter inaccuracy. In view of this, we propose a clustered scenario-tree approach, which accommodates the parameter inaccuracy problem in the context of a scenario tree.

► Proposed a new kind of scenario tree, called “cluster tree”.
► It accommodates the parameter inaccuracy in the context of a scenario tree.
► The idea is illustrated with portfolio selection problems.
► Three risk measures are considered: probability, downside risk and CVaR.
► OR techniques include fractional programming, interior point methods and SOCP.