# On optimal tracking portfolio in incomplete markets: The reinforcement learning approach

arXiv: https://arxiv.org/abs/2311.14318 · HTML: https://mlsanity.com/paper/2311.14318/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2023.

## Built on by (most cited first, 9 of 9)

- [Unified continuous-time q-learning for mean-field game and mean-field control problems](https://mlsanity.com/paper/2407.04521/) (2024)
- [Continuous-time q-Learning for Jump-Diffusion Models under Tsallis Entropy](https://mlsanity.com/paper/2407.03888/) (2024)
- [Deterministic Policy Gradient for Reinforcement Learning with Continuous Time and State](https://mlsanity.com/paper/2509.23711/) (2025)
- [Continuous-time reinforcement learning for optimal switching over multiple regimes](https://mlsanity.com/paper/2512.04697/) (2025)
- [Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations](https://mlsanity.com/paper/2604.27372/) (2026)
- [Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithms](https://mlsanity.com/paper/2604.27378/) (2026)
- [Deterministic Policy Gradient for Learning Equilibrium in Time-Inconsistent Control Problems](https://mlsanity.com/paper/2606.11798/) (2026)
- [A Reinforcement Learning Framework for Some Singular Stochastic Control Problems](https://mlsanity.com/paper/2506.22203/) (2025)
- [Reinforcement learning for irreversible reinsurance problems: the randomized singular control approach](https://mlsanity.com/paper/2512.02769/) (2025)

## Abstract (arXiv)

This paper studies an infinite horizon optimal tracking portfolio problem using capital injection in incomplete market models. The benchmark process is modelled by a geometric Brownian motion with zero drift driven by some unhedgeable risk. The relaxed tracking formulation is adopted where the fund account compensated by the injected capital needs to outperform the benchmark process at any time, and the goal is to minimize the cost of the discounted total capital injection. When model parameters are known, we formulate the equivalent auxiliary control problem with reflected state dynamics, for which the classical solution of the HJB equation with Neumann boundary condition is obtained explicitly. When model parameters are unknown, we introduce the exploratory formulation for the auxiliary control problem with entropy regularization and develop the continuous-time q-learning algorithm in models of reflected diffusion processes. In some illustrative numerical example, we show the satisfactory performance of the q-learning algorithm.