Direct data-based decision making under uncertainty

In a typical one-period decision making model under uncertainty, unknown consequences are modeled as random variables. However, accurately estimating probability distributions of the involved random variables from historical data is rarely possible. As a result, decisions made may be suboptimal or even unacceptable in the future. Also, an agent may not view data occurred at different time moments, e.g. yesterday and one year ago, as equally probable. The agent may apply a so-called “time” profile (weights) to historical data. To address these issues, an axiomatic framework for decision making based directly on historical time series is presented. It is used for constructing data-based analogues of mean-variance and maxmin utility approaches to optimal portfolio selection.