Independent research
Mathematical physics × Quant finance
Open access
2026
HFThot Research Lab
Independent research at the intersection of mathematical physics and quantitative finance.
Five public working papers, full PDFs, BibTeX citations, an open peer-feedback channel,
and a transparent roadmap toward journal submission.
M. Alvarez — Independent Researcher
HFThot Research Lab · Switzerland 🇨🇭 · 2026
Systems & physics papers
Alongside the quantitative-finance working papers above, the same lab publishes the open-source
systems and mathematical-physics libraries used to build them: Polarway,
pysic-rs and
optimiz-rs, each with its own arXiv-style paper living in its own repository.
Systems
Data engineering
Railway-oriented programming
Category theory
Polarway: Railway-Oriented Data Processing on a Lakehouse Substrate
M. Alvarez · HFThot Research Lab · 2026 · 16 pp. (+ 23 pp. extended whitepaper)
Polarway applies Railway-Oriented Programming to analytical pipelines — every transformation returns an explicit success/failure value, so error handling composes instead of being bolted on through exceptions. Built as an extension of the Polars columnar engine, it adds a Delta-Lake-backed lakehouse with ACID transactions and time travel, a domain-agnostic event bus, network-native streaming sources (WebSocket, REST, gRPC), and a Spark DataFrame compatibility layer. On a single node with 5M rows, the engine is 3.4–8.7× faster than PySpark on scan/aggregation/join/windowing — while reporting honestly where it loses: PySpark is 1.8× faster on sort-with-top-k, and DuckDB beats it on four of five queries. The extended whitepaper adds full proofs that Polarway's pipeline composition forms a genuine Kleisli category and that its streaming aggregations are correct exactly when their combiner is a monoid homomorphism — the algebraic condition behind constant-memory processing of datasets larger than RAM — together with a structural comparison against Spark, Kafka, Cloudera and Databricks.
📋 BibTeX
@techreport{alvarez2026polarway,
author = {Alvarez, M.},
title = {Polarway: Railway-Oriented Data Processing on a Lakehouse Substrate},
institution = {HFThot Research Lab},
year = {2026},
url = {https://hfthot-lab.eu/papers/polarway-arxiv.pdf}
}
Systems
Mathematical physics
Rust / Python
Validation discipline
pysic-rs: A Validated Mathematical-Physics Engine in Rust
M. Alvarez · HFThot Research Lab · 2026 · 13 pp.
pysic-rs is a CPU-only mathematical-physics library in Rust exposed to Python via PyO3, covering special functions, linear algebra, ODE/PDE solvers, quantum mechanics, general relativity, gauge theory, topology and electromagnetism — built around one methodological commitment: every routine is graded against a closed-form or tabulated reference value rather than demonstrated on a plausible-looking plot. Applying that discipline to a pedagogical walk-through connecting Schrödinger, Dirac, Maxwell/Aharonov–Bohm, the ADM constraints and Wheeler–DeWitt exposed eight incorrect routines already in the library's own code — including a Dirac propagator whose norm grew to 3.6×1057. The paper also sketches, honestly against the real (currently unfinished) source of the sibling polarway-distributed project, what it would take to run pysic-rs parameter sweeps in distributed mode with optimiz-rs as the numerical scaffolding — presented explicitly as an unshipped wiring pattern, not a benchmarked feature.
📋 BibTeX
@techreport{alvarez2026pysicrs,
author = {Alvarez, M.},
title = {pysic-rs: A Validated Mathematical-Physics Engine in Rust, and What Grading It Against Closed Forms Revealed},
institution = {HFThot Research Lab},
year = {2026},
url = {https://hfthot-lab.eu/papers/pysic-rs-validated-physics-engine.pdf}
}
Systems
Numerical primitives
Rust / Python
optimiz-rs: A Rust-Backed Library of Composable Numerical Primitives
M. Alvarez · HFThot Research Lab · 2026 · 18 pp.
optimiz-rs is a Rust library of numerical primitives — hidden Markov models, backward stochastic differential equations, McKean–Vlasov diffusions, path signatures, persistent homology, Hawkes processes and robust estimators — exposed to Python through a stable PyO3 facade and distributed on both PyPI and crates.io. The paper gives complete mathematical derivations of the core primitives, validates the implementation by reproducing Sznitman's propagation-of-chaos convergence rate on a mean-reverting McKean–Vlasov flow, and reports honest single-thread benchmarks showing 1.7–67.7× wall-clock speedups over pure-Python/NumPy/SciPy baselines on intrinsically sequential workloads.
📋 BibTeX
@techreport{alvarez2026optimizrs,
author = {Alvarez, M.},
title = {optimiz-rs: A Rust-Backed Library of Composable Numerical Primitives for Quantitative Finance},
institution = {HFThot Research Lab},
year = {2026},
url = {https://hfthot-lab.eu/papers/optimiz-rs-system.pdf}
}
Physics
Gauge theory
Prerequisites
Prerequisites for Yang–Mills Theory and the Mass Gap Problem
M. Alvarez · HFThot Research Lab · 2026 · 29 pp.
A self-contained mathematical primer for the companion article “Yang–Mills: Why a Million-Dollar Problem Has Resisted for 70 Years.” Builds, from first principles, the machinery that article assumes: Lie groups and algebras, principal bundles, connections and curvature (the geometric meaning of $A_\mu$ and $F_{\mu\nu}$), the variational derivation of the Yang–Mills field equations, the Wightman axioms needed to state the Clay Millennium mass-gap problem rigorously, the one-loop derivation of asymptotic freedom, the topological classification of instantons via the Bogomolny bound, and the spontaneous-symmetry-breaking computation behind the Higgs mechanism — closing with a section-by-section roadmap back to the article. Full derivations, worked examples, and exercises with solutions throughout.
📋 BibTeX
@techreport{alvarez2026yangmillsprereqs,
author = {Alvarez, M.},
title = {Prerequisites for Yang--Mills Theory and the Mass Gap Problem},
institution = {HFThot Research Lab},
year = {2026},
url = {https://hfthot-lab.eu/papers/yang-mills-prerequisites.pdf}
}
Public working papers
Each working paper is released as an open PDF, accompanied by a companion course on
hfthot-lab.eu/courses
and a blog summary. We welcome peer feedback by email.
WP1
Mean-field games
McKean–Vlasov
Optimal allocation
Optimal Trading via Mean-Field Games & MCMC
M. Alvarez · HFThot Research Lab · 2026 · 32 pp.
We formulate optimal portfolio allocation in the presence of self-induced market impact as a mean-field game (MFG) of McKean–Vlasov type. The Hamilton–Jacobi–Bellman / Fokker–Planck system is solved by a particle method coupled to an MCMC sampler over the population distribution. We prove convergence of the discretised system under a monotonicity condition on the running cost and provide explicit sample-complexity bounds. A numerical study on a synthetic universe shows that the MFG-aware allocator outperforms classical mean-variance both in Sharpe and in turnover-stability across regime switches.
📋 BibTeX
@techreport{alvarez2026wp1,
author = {Alvarez, M.},
title = {Optimal Trading via Mean-Field Games and {MCMC}},
institution = {HFThot Research Lab},
number = {WP1},
year = {2026},
url = {https://hfthot-lab.eu/papers/wp1-mean-field-games.pdf}
}
WP2
Rough volatility
Path signatures
Heston
Rough Heston & Signature Methods for Volatility Arbitrage
M. Alvarez · HFThot Research Lab · 2026 · 38 pp.
The rough Heston model captures key empirical features of the implied-volatility surface — short-term skew, term-structure of vol-of-vol, and roughness exponent $H \approx 0.1$ — that classical Heston cannot reproduce. We derive an efficient calibration scheme that combines fractional ODE numerics with a path-signature representation of forward variance curves. The signature embedding turns the calibration into a smooth optimisation in feature space, yielding a 10–30× speed-up over Fourier-based calibrations on liquid surfaces. We show empirically that the rough-Heston / signature pipeline closes the calibration gap on SPX, EUR/USD, and BTC option surfaces, and we use it to build a model-free volatility-arbitrage indicator with documented backtest performance on synthetic paths.
📋 BibTeX
@techreport{alvarez2026wp2,
author = {Alvarez, M.},
title = {Rough {H}eston and Signature Methods for Volatility Arbitrage},
institution = {HFThot Research Lab},
number = {WP2},
year = {2026},
url = {https://hfthot-lab.eu/papers/wp2-rough-heston-signatures.pdf}
}
WP3
Stochastic control
HJB
Adaptive Portfolio Construction & Execution
M. Alvarez · HFThot Research Lab · 2026 · 30 pp.
A stochastic-control framework that fuses regime detection, optimal allocation, and execution-aware optimisation into a single Hamilton–Jacobi–Bellman recursion. The optimal trading rate is computed self-consistently with execution friction, eliminating the artificial split between portfolio construction and execution scheduling. Convergence of a policy-iteration scheme is proven; a deep-Galerkin variant is provided for high-dimensional regimes.
📋 BibTeX
@techreport{alvarez2026wp3,
author = {Alvarez, M.},
title = {Adaptive Portfolio Construction and Execution},
institution = {HFThot Research Lab},
number = {WP3},
year = {2026},
url = {https://hfthot-lab.eu/papers/wp3-adaptive-portfolio.pdf}
}
WP4
Volatility surfaces
SVI / SSVI
Dispersion
Options Portfolio Labs — Volatility Arbitrage at Scale
M. Alvarez · HFThot Research Lab · 2026 · 42 pp.
A unified pricing-and-hedging framework for systematic options desks: arbitrage-free SSVI surface calibration, regime-conditioned dispersion signals, and a Greeks-tensor risk budget. We provide a constrained-QP hedger that respects both transaction costs and Greek caps, and demonstrate the framework on an SPX-vs-constituent dispersion lab.
📋 BibTeX
@techreport{alvarez2026wp4,
author = {Alvarez, M.},
title = {Options Portfolio Labs: Volatility Arbitrage at Industrial Scale},
institution = {HFThot Research Lab},
number = {WP4},
year = {2026},
url = {https://hfthot-lab.eu/papers/wp4-options-portfolio-labs.pdf}
}
Per-paper journal readiness scorecard
Self-assessment of each paper's readiness for submission to a peer-reviewed journal.
Updated April 2026. Green = ready; Amber = needs targeted work; Red = significant gap.
| Criterion |
WP1 — Mean-Field Games |
WP2 — Rough Heston & Signatures |
| Mathematical rigor (theorems / proofs) |
● complete |
● complete |
| Novelty vs. existing literature |
● MFG + MCMC pairing is novel in finance context |
● SVI calibration novelty needs sharper positioning |
| Empirical validation on real data |
● synthetic only; needs SPX or crypto study |
● SPX/EUR-USD/BTC validation in companion notebook |
| Reproducibility (open code, data, seeds) |
● notebook + optimiz-rs public |
● notebook + optimiz-rs public |
| Comparison with existing methods |
● needs comparison to Cardaliaguet et al. (2019) |
● compared to Heston, SABR, classical SVI |
| Length / structure for journal format |
● condense from 32 pp. to ~25 for QF |
● trim from 38 pp. to ~30 for MathFin |
| Targeted journal |
Quantitative Finance (T&F) or SIAM J. Financial Math. |
Mathematical Finance or Finance & Stochastics |
| Estimated time to submission |
● 6–8 weeks (real-data study + comp.) |
● 4–6 weeks (length trim + final figures) |
The plan is to submit WP2 first (faster path to reviewer feedback), incorporating learnings before WP1 follows.