# Multi-Period Trading via Convex Optimization

arXiv: https://arxiv.org/abs/1705.00109 · HTML: https://mlsanity.com/paper/1705.00109/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2017.

## Built on by (most cited first, 21 of 21)

- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Deep Learning Statistical Arbitrage](https://mlsanity.com/paper/2106.04028/) (2021)
- [Learning context-aware adaptive solvers to accelerate quadratic programming](https://mlsanity.com/paper/2211.12443/) (2022)
- [Explainable Deep Reinforcement Learning for Portfolio Management: An Empirical Approach](https://mlsanity.com/paper/2111.03995/) (2021)
- [Two-step Lookahead Bayesian Optimization with Inequality Constraints](https://mlsanity.com/paper/2112.02833/) (2021)
- [Advancing Investment Frontiers: Industry-grade Deep Reinforcement Learning for Portfolio Optimization](https://mlsanity.com/paper/2403.07916/) (2024)
- [Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding](https://mlsanity.com/paper/2512.01565/) (2025)
- [Markov Decision Processes under Model Uncertainty](https://mlsanity.com/paper/2206.06109/) (2022)
- [Stochastic Bayesian Optimization with Unknown Continuous Context Distribution via Kernel Density Estimation](https://mlsanity.com/paper/2312.10423/) (2023)
- [An Efficient Unsupervised Framework for Convex Quadratic Programs via Deep Unrolling](https://mlsanity.com/paper/2412.01051/) (2024)
- [A Penalty Approach for Differentiation Through Black-Box Quadratic Programming Solvers](https://mlsanity.com/paper/2602.14154/) (2026)
- [A Learnheuristic Approach to A Constrained Multi-Objective Portfolio Optimisation Problem](https://mlsanity.com/paper/2304.06675/) (2023)
- [Robust portfolio optimization for recommender systems considering uncertainty of estimated statistics](https://mlsanity.com/paper/2406.10250/) (2024)
- [Plan Before You Trade: Inference-Time Optimization for RL Trading Agents](https://mlsanity.com/paper/2605.12653/) (2026)
- [Deep Reinforcement Learning and Convex Mean-Variance Optimisation for Portfolio Management](https://mlsanity.com/paper/2203.11318/) (2022)
- [Intelligent Systematic Investment Agent: an ensemble of deep learning and evolutionary strategies](https://mlsanity.com/paper/2203.13125/) (2022)
- [Pareto Driven Surrogate (ParDen-Sur) Assisted Optimisation of Multi-period Portfolio Backtest Simulations](https://mlsanity.com/paper/2209.13528/) (2022)
- [CatBOX: A Categorical-Continuous Bayesian Optimization with Spectral Mixture Kernels for Accelerated Catalysis Experiments](https://mlsanity.com/paper/2505.17393/) (2025)
- [Integrated Prediction and Multi-period Portfolio Optimization](https://mlsanity.com/paper/2512.11273/) (2025)
- [Ensemble Distributionally Robust Bayesian Optimisation with Continuous Context](https://mlsanity.com/paper/2605.07565/) (2026)
- [Robust Control under Stationary Ambiguity](https://mlsanity.com/paper/2608.04832/) (2026)

## Abstract (arXiv)

We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The single-period method traces back to Markowitz; the multi-period methods trace back to model predictive control. Our contribution is to describe the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. In this paper we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper.