---
title: "Neural solvers for continuous-time finance (research idea)"
description: "Continuous-time models built on the Hamilton-Jacobi-Bellman equation are rising in the finance journals, while neural operators and physics-informed networks that solve such equations are growing in AI. All five recent papers that pair the two are in AI journals. Can these solvers make richer portfolio and asset-pricing models usable?"
url: https://scholar4ai.com/ideas/neural-solvers-for-continuous-time-finance
markdown_url: https://scholar4ai.com/ideas/neural-solvers-for-continuous-time-finance.md
license: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/)
share_text: "Continuous-time models built on the Hamilton-Jacobi-Bellman equation are rising in the finance journals, while neural operators and physics-informed networks that solve such equations are growing in AI."
date: "2026-10-23"
updated: "2026-10-23"
status: "seed"
tags: ["finance", "ai", "methods"]
keywords: ["Hamilton-Jacobi-Bellman equation", "neural operators", "physics-informed neural networks"]
---

# Neural solvers for continuous-time finance

Continuous-time models built on the Hamilton-Jacobi-Bellman equation are rising in the finance journals, while neural operators and physics-informed networks that solve such equations are growing in AI. All five recent papers that pair the two are in AI journals. Can these solvers make richer portfolio and asset-pricing models usable?

## What prompted this

In the finance journals, "Hamilton-Jacobi-Bellman equation" had 8 papers in July–September 2026 against about 2 expected (see the [finance dashboard](/categories/finance)); the Bellman equation is also on the [equation ranking](/rankings/equations)'s list. In the AI journals, "neural operators" grew (9 against 3), and "physics-informed neural networks" appears on 84 papers since October 2025. Of the 70 papers with an HJB, portfolio-choice or optimal-investment keyword, 5 also carry a neural-network or machine-learning keyword, and all 5 are in AI journals.

## Questions

- Can neural solvers handle portfolio problems with many assets, frictions or stochastic volatility that grid methods cannot?
- How accurate are they where closed forms exist, and do the errors matter more for policies than for values?
- Can a solver trained once (an operator) let researchers estimate structural models that need to be solved thousands of times?

## Data that could help

Benchmark problems with known solutions, and calibrations from standard asset-pricing models.

## Next step

Solve a portfolio problem with stochastic volatility that has a known solution using a physics-informed network, and compare the optimal policies.

## Related research activity

*The keywords this note follows, in the tracked finance, accounting, economics, management, operations research and AI journals as of 2026-10-26*

| Keyword | Papers, last 30 days | Rank | Papers per month, Oct 23 – Oct 26* | Papers, last 36 months |
|---|---:|---:|---|---:|
| Hamilton-Jacobi-Bellman equation | 1 | #2881 | 2, 0, 6, 5, 4, 1, 3, 5, 4, 2, 4, 1, 3, 1, 1, 3, 0, 0, 6, 4, 3, 4, 6, 2, 3, 0, 4, 6, 2, 2, 5, 3, 2, 3, 2, 4, 1 | 106 |
| neural operators | 0 | – | 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 3, 1, 0, 0, 1, 3, 0, 1, 2, 2, 2, 4, 0, 5, 0 | 34 |
| physics-informed neural networks | 8 | #188 | 1, 1, 5, 4, 4, 1, 4, 5, 0, 0, 3, 6, 3, 2, 3, 7, 3, 5, 5, 6, 7, 7, 9, 3, 4, 3, 11, 9, 10, 9, 7, 6, 11, 8, 12, 8, 7 | 192 |

## Cite this page

Scholar4AI. (2026). Neural solvers for continuous-time finance. Journal Research Rankings. Retrieved October 23, 2026, from https://scholar4ai.com/ideas/neural-solvers-for-continuous-time-finance

```bibtex
@misc{scholar4ai-ideas-neural-solvers-for-continuous-time-finance,
  author = {{Scholar4AI}},
  title = {Neural solvers for continuous-time finance},
  year = {2026},
  howpublished = {\url{https://scholar4ai.com/ideas/neural-solvers-for-continuous-time-finance}},
  urldate = {2026-10-23},
  note = {Journal Research Rankings; data from OpenAlex (CC0); licensed CC BY-NC 4.0}
}
```

License: CC BY-NC 4.0 (https://creativecommons.org/licenses/by-nc/4.0/).