Multistage stochastic programs with a random number of stages: dynamic programming equations, solution methods, and application to portfolio selection

TL;DR

This paper introduces multistage stochastic optimization models with a random number of stages, develops dynamic programming equations, adapts the Stochastic Dual Dynamic Programming algorithm, and demonstrates improved portfolio selection strategies considering random durations.

Contribution

It extends multistage stochastic programming to include random stage counts, providing new dynamic programming formulations and solution methods applicable to portfolio management.

Findings

Policies accounting for random stage durations outperform fixed-stage policies.

The adapted SDDP algorithm effectively solves the new class of problems.

Significant gains observed in portfolio selection scenarios.

Abstract

We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and detail the Stochastic Dual Dynamic Programming algorithm to solve these equations. Finally, we consider a portfolio selection problem over an optimization period of random duration. For several instances of this problem, we show the gain obtained using a policy that takes the random duration of the number of stages into account over a policy built taking a fixed number of stages (namely the maximal possible number of stages).