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); the Bellman equation is also on the equation ranking'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.