Struct AvellanedaGueant 

pub struct AvellanedaGueant {
    pub gamma: f64,
    pub sigma: f64,
    pub kappa: f64,
    pub a: f64,
    pub q_max: usize,
}

The asymptotic approximation (infinite horizon) for the Avellaneda-Stoikov model. Based on the Gueant-Lehalle-Tapia closed-form solution.

Reference: Guéant, O., Lehalle, C. A., & Tapia, J. (2013). Dealing with the inventory risk: a solution to the market making problem.

Fields

gamma: f64

sigma: f64

kappa: f64

a: f64

q_max: usize

Inventory truncation used when evaluating the value reference.

Implementations

impl AvellanedaGueant

pub fn new(gamma: f64, sigma: f64, kappa: f64, a: f64) -> Self

pub fn with_q_max(self, q_max: usize) -> Self

Sets the inventory truncation used for the value reference.

pub fn approximate_spreads(&self, q: f64) -> (f64, f64)

Guéant-Lehalle-Tapia closed-form approximation for optimal spreads.

This approximation assumes infinite time horizon ($T \to \infty$) and small spreads, providing a stationary strategy that depends on inventory $q$ but not time $t$.

The spreads are symmetric around the mid-price, shifted by inventory: $\delta^\pm(q) \approx \text{RiskNeutral} \pm \text{InventorySkew} \cdot q$

Reference: Guéant, O., Lehalle, C. A., & Tapia, J. (2013). Dealing with the inventory risk.

pub fn stationary_theta(&self, q_max: usize, q: i32) -> f64

Stationary value function theta(q) for the reduced Avellaneda model.

The exact stationary solution of the GLT linearized HJB is the principal eigenvector v(q) of the symmetric tridiagonal operator with diagonal -alpha q^2 and off-diagonal eta, where

alpha = (kappa / 2) gamma sigma^2
eta   = a (1 + gamma/kappa)^{-(1 + kappa/gamma)}

The reduced solver works directly in theta space, with v(q) = exp(kappa theta(q)). The value is normalized so theta(0) = 0, which removes the one-parameter translation invariance of the stationary HJB. Only differences theta(q) - theta(q') are invariant under the normalization and therefore meaningful.

Panics

Panics if q is outside [-q_max, q_max].

pub fn stationary_spreads(&self, q_max: usize, q: i32) -> (f64, f64)

Stationary bid/ask spreads implied by the principal-eigenvector value.

The bid spread is base + (theta(q) - theta(q+1)) / 2 adjusted for the half-inventory convention, and the ask spread is the mirror around the base spread. This matches the approximate_spreads small-gamma limit.

Trait Implementations

impl AnalyticalSolution<2> for AvellanedaGueant

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

Returns the theoretical value function V(t, state)

fn optimal_controls(&self, _t: f64, state: &[f64; 2]) -> MarketMakingControl

Returns the optimal controls (intensities) at (t, state)