# 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.

## Key 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).

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Source: https://tomesphere.com/paper/1803.06034