solver/analytical/drift/approximations/
mod.rs

1use crate::analytical::traits::AnalyticalSolution;
2use crate::models::traits::ControlOutput;
3
4/// The asymptotic approximation for the Avellaneda-Stoikov model with Drift.
5pub struct AvellanedaDriftApprox {
6    pub gamma: f64,
7    pub sigma: f64,
8    pub kappa: f64,
9    pub a: f64,
10    pub mu: f64,
11}
12
13impl AvellanedaDriftApprox {
14    pub fn new(gamma: f64, sigma: f64, kappa: f64, a: f64, mu: f64) -> Self {
15        Self {
16            gamma,
17            sigma,
18            kappa,
19            a,
20            mu,
21        }
22    }
23
24    pub fn approximate_spreads(&self, q: f64) -> (f64, f64) {
25        let const_term = (1.0 / self.gamma) * (1.0 + self.gamma / self.kappa).ln();
26        let factor = (self.sigma.powi(2) * self.gamma / (2.0 * self.kappa * self.a)).sqrt()
27            * (1.0 + self.gamma / self.kappa).powf(0.5 * (1.0 + self.kappa / self.gamma));
28
29        let term_bid = -self.mu / (self.gamma * self.sigma.powi(2)) + (2.0 * q + 1.0) / 2.0;
30        let term_ask = self.mu / (self.gamma * self.sigma.powi(2)) - (2.0 * q - 1.0) / 2.0;
31
32        let delta_bid = const_term + term_bid * factor;
33        let delta_ask = const_term + term_ask * factor;
34
35        (delta_bid, delta_ask)
36    }
37}
38
39impl AnalyticalSolution<2> for AvellanedaDriftApprox {
40    fn value_function(&self, _t: f64, _state: &[f64; 2]) -> f64 {
41        0.0
42    }
43
44    fn optimal_controls(&self, _t: f64, state: &[f64; 2]) -> ControlOutput<2> {
45        let q = state[0];
46        let (d_bid, d_ask) = self.approximate_spreads(q);
47
48        let lambda_bid = self.a * (-self.kappa * d_bid).exp();
49        let lambda_ask = self.a * (-self.kappa * d_ask).exp();
50
51        let flow = lambda_bid * d_bid + lambda_ask * d_ask;
52
53        ControlOutput {
54            lambda_plus: [lambda_bid, 0.0],
55            lambda_minus: [lambda_ask, 0.0],
56            flow,
57        }
58    }
59}
solver/analytical/drift/approximations/mod.rs

solver/analytical/drift/approximations/
mod.rs
