# Risk averse stochastic programming: time consistency and optimal stopping

arXiv: https://arxiv.org/abs/1808.10807 · HTML: https://mlsanity.com/paper/1808.10807/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2018.

## Built on by (most cited first, 4 of 4)

- [Soft Robust MDPs and Risk-Sensitive MDPs: Equivalence, Policy Gradient, and Sample Complexity](https://mlsanity.com/paper/2306.11626/) (2023)
- [Two steps to risk sensitivity](https://mlsanity.com/paper/2111.06803/) (2021)
- [Bayesian Risk-Sensitive Policy Optimization For MDPs With General Loss Functions](https://mlsanity.com/paper/2509.15509/) (2025)
- [How much Data do We Need? Sequential Data Collection for Stochastic Programming](https://mlsanity.com/paper/2607.10207/) (2026)

## Abstract (arXiv)

Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically or time consistent and introduces stopping time risk measures. It turns out that the paradigm of time consistency is in conflict with various desirable, classical properties of general risk measures.