Implementation Matrix

This page catalogues every configurable option across the three crates and shows which combinations are compatible. Use it to determine what model, solver, and engine setup fits your use case.

Models

The solver crate provides 9 pre-built optimal control models. Each implements ControlProblem<N> for a specific state dimension and set of dynamics; models solved on a diffusive grid also implement the FD-specific PdeProblem<N> transport contract. All models are solved rigorously — they discretize the exact HJB PDE without approximation. See Rigor Reference for the full mapping of HJB to method.

Model	N	State variables	HJB solved	FD	BSDE	Rigor
`AvellanedaStoikov`	2	q, S	CARA AS HJB	Yes	Yes	Rigorous
`AvellanedaDrift`	2	q, S	CARA AS HJB + price drift	Yes	Yes	Rigorous
`AvellanedaImpact`	2	q, S	CARA AS HJB + market impact	Yes	Yes	Rigorous
`AvellanedaHawkes`	2	q, lambda	CARA AS HJB + unilateral Hawkes	Yes	Yes	Rigorous
`BilateralHawkes`	3	q, lambda+, lambda-	CARA AS HJB + bilateral Hawkes	Yes	Yes	Rigorous
`BilateralHawkesOFI`	3	q, lambda+, lambda-	CARA AS HJB + bilateral Hawkes + OFI	Yes	Yes	Rigorous
`Heston`	2	q, v	CARA AS HJB + Heston vol	Yes	Yes	Rigorous
`HestonHawkes`	3	q, v, lambda	CARA AS HJB + Heston + Hawkes	Yes	Yes	Rigorous
`AmericanPut`	1	S	Optimal stopping HJB	Yes	No	Rigorous

Terminal conditions

Condition	Value at expiry	Supported by
`Zero`	\(V(T) = 0\) for all states	All 9 models
`LiquidationCost`	\(V(T) = -\lvert q \rvert \cdot half\_spread\)	AvellanedaHawkes, BilateralHawkes, BilateralHawkesOFI, Heston

Models that do not expose with_terminal_condition have hardcoded terminal values (usually zero, or a model-specific expression like -0.5*xi*q^2 for AvellanedaImpact). To apply uniform terminal liquidation at the backtest level, use run_backtest_with_liquidation from the engine.

Price behaviours captured

Behaviour	Models
Constant volatility	AvellanedaStoikov, AvellanedaDrift, AvellanedaImpact
Stochastic volatility	Heston, HestonHawkes
Mean-reverting intensity	AvellanedaHawkes, BilateralHawkes, BilateralHawkesOFI, HestonHawkes
Jump diffusion on price	(via `market_model` processes fed to engine, not via solver models)
Permanent market impact	AvellanedaImpact, BilateralHawkesOFI
Order flow imbalance	BilateralHawkesOFI (eta_ofi > 0)
Drifting mid-price	AvellanedaDrift

Solvers

Both numerical solvers accept any ControlProblem<N> implementation. The grid-based PolicyIterationSolver additionally requires PdeProblem<N> for the implicit, Crank-Nicolson, and Strang-ADI schemes; explicit Euler only needs ControlProblem.

Solver	Method	Best for	Time discretisation
`PolicyIterationSolver`	Finite difference on a grid	N <= 3, high accuracy	Implicit, Explicit, Crank-Nicolson, Strang ADI
`BsdeSolver`	Least-squares Monte Carlo regression	N >= 3, scales better with dimension	Forward-backward with basis functions

Solver	Scheme options	Linear solver
`PolicyIterationSolver`	`Implicit` (default: Crank-Nicolson), `Explicit`, `StrangAdi`	SOR, Thomas (tridiagonal), LAPACK dgtsv
`BsdeSolver`	Polynomial basis (Power, Hermite, Chebyshev, Laguerre), degree 1-6, scaling wrapper	Custom regression (SVD via faer)

Engine strategies

All strategies implement Strategy and consume Observation (filtered by ObservationFilter) to emit OrderRequests.

Strategy	Table dims	Solution source	HJB solved	Rigor
`AvellanedaStoikovExactStrategy`	2D	Exact matrix ODE tables	CARA AS HJB	Rigorous
`AvellanedaStoikovHestonStrategy`	3D	Precomputed FDM Heston tables	CARA AS HJB + Heston vol	Rigorous
`AvellanedaStoikovHawkesStrategy`	3D	Precomputed FDM Hawkes tables	CARA AS HJB + Hawkes	Rigorous
`AvellanedaStoikovBilateralHawkesStrategy`	4D	Precomputed FDM BilateralHawkes tables	CARA AS HJB + bilateral Hawkes	Rigorous
`AvellanedaStoikovBilateralHawkesOFIStrategy`	4D	Precomputed FDM BilateralHawkesOFI tables	CARA AS HJB + bilateral Hawkes + OFI	Rigorous
`AvellanedaStoikovStrategy`	—	AS analytical formula	None (inline approximation)	Approximation
`ConstantSymmetricStrategy`	—	Fixed half-spread	None	Heuristic
`KellyStrategy`	2D	Online mu/sigma est. + AS formula	None (CARA ansatz, no log-utility HJB)	Heuristic
`KellyRigorousStrategy`	3D	Precomputed FDM Kelly tables	Log-utility HJB (x-reduced)	Rigorous
`ZeroIntelligenceStrategy`	—	Uniform random half-spread	None	Heuristic
`RandomStrategy`	—	Random side + price jitter	None	Heuristic
`SignalEngineStrategy`	—	MA / RSI / multi-signal voting	None	Heuristic
`ExternalStrategy`	—	Externally injected	N/A	N/A

Strategy to model mapping

Strategy	Compatible solver model
`AvellanedaStoikovStrategy`	AvellanedaStoikov, AvellanedaDrift
`AvellanedaStoikovExactStrategy`	AvellanedaStoikov
`AvellanedaStoikovHestonStrategy`	Heston
`AvellanedaStoikovHawkesStrategy`	AvellanedaHawkes
`AvellanedaStoikovBilateralHawkesStrategy`	BilateralHawkes
`AvellanedaStoikovBilateralHawkesOFIStrategy`	BilateralHawkesOFI
`ConstantSymmetricStrategy` / ZI / Random / Kelly	Any (model-agnostic)

Matchers

Two matcher implementations determine how limit orders get filled.

Matcher	Fill mechanisms	Hawkes support	Features
`SimpleMatcher`	Aggressive crossing at BBO	No	Deterministic, zero configuration
`StochasticMatcher`	Aggressive + sweep + Poisson arrival	Unilateral or bilateral	Configurable k, a, alpha, beta

StochasticMatcher Hawkes modes

Mode	Builder	a_eff(t)	Parameters exposed
No Hawkes	default	a (constant)	—
Unilateral	`.with_hawkes(alpha, beta)`	a + excitation(t)	`hawkes_intensity`
Bilateral	`.with_bilateral_hawkes(alpha, beta)`	Separate per side	`hawkes_buy_intensity`, `hawkes_sell_intensity`

Data sources

Source	Processes	Output	Ground truth
`SimulatedDataSource<P>`	GBM, Heston, Bates	BBO + vol + drift + params	Optional (filtered by `ObservationFilter`)
`ParquetDataSource`	File replay	BBO only	None

Backtesting

Function	Terminal liquidation	Custom lookback	Use case
`run_backtest`	No	No (default 10)	Default path
`run_backtest_with_liquidation`	Yes (\(\lvert q \rvert \cdot half\_spread\))	No	Consistent with `LiquidationCost` terminal condition
`run_backtest_lookback`	No	Yes (custom steps)	Custom adverse selection window

BacktestResult metrics

Return, annualised return, volatility, Sharpe, Sortino, max drawdown, total trades, final equity, mean/max/min inventory, adverse selection (bps), realised edge (bps), inventory variance, PnL spread, PnL directional, fill buy/sell counts, mean hold time, terminal liquidation cost.

Observation filtering

Mode	Constructor	Visible to strategy
Transparent	`transparent()`	BBO, portfolio, volatility, drift, all parameters
Opaque	`opaque()`	BBO, portfolio only
Partial	Struct fields	BBO, portfolio, selected parameters via whitelist

VecEnv

Field	Purpose
Process	GBM, Heston, or Bates (configurable via `VecEnvProcess` enum)
Matcher	`StochasticMatcher` with bilateral Hawkes when \(hawkes\_alpha > 0\)
Strategy	`ExternalStrategy` (actions injected per step)
State (5D GBM)	[mid, inventory, lambda_buy, lambda_sell, time]
State (6D Heston/Bates)	[mid, inventory, variance, lambda_buy, lambda_sell, time]
Action (2D)	[bid_distance, ask_distance] from mid
Reward	PnL or DiffSharpe, minus inventory penalty
Parallelism	Sequential across N independent envs

market-solve