Multiperiod interval-based stochastic dominance with application to dynamic portfolios

We consider a multi-stage generalization of the interval-based stochastic dominance (ISD) principles introduced by Liu et al. [Interval-based stochastic dominance: Theoretical framework and application to portfolio choices. Ann. Oper. Res., 2021, 307, 329–361]. The ISD criterion was motivated specifically in a financial context to allow for contiguous integer SD orders on different portions of a portfolio return distribution against a benchmark distribution. A continuous spanning of SD conditions between first-, second-, and third-order stochastic dominance was introduced in that context, relying on a reference point. Here, by extending the partial order to random data processes, we apply ISD conditions to a multi-period portfolio selection problem and verify the modeling and computational implications of such an extension. Several theoretical and methodological issues arise in this case that motivate this contribution. The problem is formulated in scenario form as a multistage stochastic recourse program, and we study two possible generalizations of ISD principles in which we either enforce ISD constraints at each stage, independently from the scenario tree process evolution, or we do so conditionally along the scenario tree. We present a comprehensive set of computational results to show that, depending on the benchmark investment policy and the adopted ISD formulation, stochastic dominance conditions of first- or second-order can be enforced dynamically over a range of possible values of the reference point, and their solution carries a specific rationale. The computational constraints induced by the multistage ISD formulation are also emphasized and discussed in detail.