Multi-period portfolio selection with interval-based conditional value-at-risk

We propose a multi-period mean-risk portfolio model based as a risk measure on the interval conditional value at risk (ICVaR). The ICVaR was introduced in Liu et al. (Ann Op Res 307:329–361, 2021) in a strict relationship with second-order stochastic dominance and adopted as risk measure in the formulation of a static portfolio optimization problem: in this article we reconsider its key properties and specify a multistage portfolio model based on the trade-off between expected wealth and terminal ICVaR. The definition of this risk measure depends on a reference point, that by discriminating between contiguous stochastic dominance orders motivated in Liu et al. (2021) the introduction of interval stochastic dominance (ISD) of the first and second-order specifically in a financial context. We develop from there in this article and present a set of results that help characterizing rigorously the relationship between the solution of the multistage stochastic programming portfolio problem and the underlying ISD principles. An extended set of computational results is presented to validate in- and out-of-sample a set of mathematical results and the modeling framework over the 2021–2022 period.