Struct AvellanedaHawkes 

pub struct AvellanedaHawkes {
    pub gamma: f64,
    pub sigma: f64,
    pub kappa: f64,
    pub alpha: f64,
    pub beta: f64,
    pub mu: f64,
    pub lambda_step: f64,
    pub dq: f64,
    pub terminal_condition: TerminalCondition,
    pub q_min: f64,
    pub q_max: f64,
    pub terminal_liquidation_half_spread: Option<f64>,
}

Avellaneda-Stoikov model with Hawkes Process for order arrival intensity.

State Space: [Inventory (q), Intensity (lambda)]

• q: Discrete inventory level
• lambda: Continuous order arrival intensity

Dynamics:

• q: Jumps ±1 upon fills.
• lambda: Mean-reverting jump-diffusion (approximated). d(lambda) = beta * (mu - lambda) * dt + alpha * dN_market where N_market is the market order counting process with intensity lambda.

The solver uses a grid-based approach. We approximate the Hawkes dynamics on the lambda dimension using an upwind finite difference scheme mapped to the solver’s jump interface.

Fields

gamma: f64

sigma: f64

kappa: f64

alpha: f64

beta: f64

mu: f64

lambda_step: f64

dq: f64

Grid step size for inventory dimension (set from grid.dx[0] for FD).

terminal_condition: TerminalCondition

Terminal condition V(T, q, lambda). Defaults to Zero.

q_min: f64

Minimum inventory (lower hard boundary). Defaults to -infinity (no constraint).

q_max: f64

Maximum inventory (upper hard boundary). Defaults to +infinity (no constraint).

terminal_liquidation_half_spread: Option<f64>

Optional terminal liquidation half-spread used when terminal_condition is LiquidationCost. If None, uses the AS base spread.

Implementations

impl AvellanedaHawkes

pub fn new( gamma: f64, sigma: f64, kappa: f64, alpha: f64, beta: f64, mu: f64, ) -> Self

pub fn with_terminal_liquidation_half_spread(self, half_spread: f64) -> Self

pub fn with_inventory_bounds(self, q_min: f64, q_max: f64) -> Self

pub fn with_terminal_condition( self, terminal_condition: TerminalCondition, ) -> Self

pub fn with_lambda_step(self, lambda_step: f64) -> Self

pub fn with_dq(self, dq: f64) -> Self

pub fn get_spreads( &self, _lambda: f64, derivs: &StateDerivatives<2>, ) -> (f64, f64)

Computes optimal spreads based on current inventory and intensity. Note: The base intensity ‘A’ from standard Avellaneda is replaced by the state variable ‘lambda’.

pub fn fill_rate_base(&self, state: &[f64; 2]) -> f64

The base arrival intensity is state-dependent: returns the current intensity state[1] (clamped above 0) for intensity-to-spread conversion.

pub fn fill_rate_decay(&self) -> f64

The fill-rate decay parameter used for intensity-to-spread conversion.

Trait Implementations

impl Clone for AvellanedaHawkes

fn clone(&self) -> AvellanedaHawkes

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl ControlProblem<2> for AvellanedaHawkes

type Control = MarketMakingControl

The action type. For Merton this is a scalar portfolio fraction; for market making it is a pair of bid/ask intensities.

fn optimize( &self, _t: f64, state: &[f64; 2], derivs: &StateDerivatives<2>, ) -> Self::Control

Returns the control that maximizes the driver at (t, state).

fn running_reward( &self, _t: f64, _state: &[f64; 2], control: &Self::Control, ) -> f64

Returns the running reward f(t,x,u).

fn bsde_driver( &self, _t: f64, state: &[f64; 2], control: &Self::Control, _derivs: &StateDerivatives<2>, dt: f64, ) -> f64

Returns the backward driver consumed by the BSDE regression solver.

fn generator( &self, _t: f64, state: &[f64; 2], _control: &Self::Control, derivs: &StateDerivatives<2>, ) -> f64

Returns the infinitesimal generator L^u V for the given control and derivative bundle.

fn terminal(&self, state: &[f64; 2]) -> f64

Terminal value g(x) at the horizon.

fn discount_rate(&self, _state: &[f64; 2]) -> f64

Discount rate r(t,x). Defaults to zero.

fn constant_discount_rate(&self) -> Option<f64>

Constant discount rate hint. Defaults to None (state dependent).

fn next_step( &self, _t: f64, state: &[f64; 2], dt: f64, noise: &[f64; 2], ) -> [f64; 2]

Advances the state one step under the optimal control at forward time t.

fn next_step_controlled( &self, _t: f64, state: &[f64; 2], control: &Self::Control, dt: f64, noise: &[f64; 2], ) -> [f64; 2]

Advances the state one step under an explicitly supplied control.

fn is_diffusion_dimension(&self, _dim: usize) -> bool

Whether a dimension is driven by Brownian diffusion.

fn gradient_step(&self, dim: usize) -> f64

Physical finite-difference step for a dimension, used by mesh-free gradient stencils.

fn driver( &self, t: f64, state: &[f64; N], control: &Self::Control, derivs: &StateDerivatives<N>, ) -> f64

Returns the full HJB driver f(t,x,u) + L^u V.

fn apply_constraint(&self, _state: &[f64; N], value: f64) -> f64

Optional pointwise constraint on the value, e.g. the early-exercise obstacle V >= payoff for an American option.

fn is_reduced_value(&self) -> bool

Whether the value this problem solves is a reduced value.

impl PdeProblem<2> for AvellanedaHawkes

fn dimension_kind(&self, dim: usize) -> DimensionKind

Discretization kind for dim.

fn transport( &self, _t: f64, state: &[f64; 2], control: &Self::Control, derivs: &StateDerivatives<2>, ) -> Transport<2>

Transport and local source for the given control and derivatives.

fn jump_kernel( &self, _t: f64, _state: &[f64; N], _control: &Self::Control, _derivs: &StateDerivatives<N>, transport: &Transport<N>, ) -> JumpKernel<N>

Jump kernel for arbitrary-amplitude jump dimensions.