Scenarios

Many models in the academic economics and finance literature are formulated in terms of distributions supported on continuous and unbounded state spaces. These continuous distributions are hard to grasp for decision makers, and they imply quantitative statements on tail events that are hard to reconcile with observed data. As a consequence, many practical applications are instead performed with a small number of scenarios that are representative of the underlying structure. This project is aimed at proposing a framework for the determination of these scenarios that suits probabilistic, statistical, and economic considerations, and is tractable and computationally efficient at the same time. Most decision problems under uncertainty can be formulated as expectations. An important requirement for the scenarios is therefore to facilitate good approximations of expectations for a large class of test functions. To accommodate smooth test functions like, for example, power utility, we propose to choose scenarios in accordance with quadrature integration rules. The nodes and weights of these scenarios turn out to be strongly related to distributions related to the solution of the truncated moment problem, that relates moments of the original distribution to an auxiliary distribution with the smallest number of states that can generate these moments.