Struct KellyHjb 

pub struct KellyHjb {
    pub sigma: f64,
    pub kappa: f64,
    pub a: f64,
    pub q_min: f64,
    pub q_max: f64,
    pub dq: f64,
}

Fields

sigma: f64

Price volatility ($\sigma$).

kappa: f64

Fill-rate decay ($k$).

a: f64

Base order arrival intensity ($A$).

q_min: f64

Minimum inventory (lower hard boundary).

q_max: f64

Maximum inventory (upper hard boundary).

dq: f64

Grid step for the inventory dimension.

Implementations

impl KellyHjb

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

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

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

Compute optimal bid/ask spreads from value-function gradients.

fwd[0] = dv/dq = v(q+1) - v(q), bwd[0] = v(q) - v(q-1) for dq=1. The x-dimension gradient enters through the finite-difference stencil on the grid and is handled by the solver’s operator.

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

The base arrival intensity used 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 KellyHjb

fn clone(&self) -> KellyHjb

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ControlProblem<2> for KellyHjb

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 is_reduced_value(&self) -> bool

Whether the value this problem solves is a reduced value.

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 next_step_controlled( &self, t: f64, state: &[f64; N], _control: &Self::Control, dt: f64, noise: &[f64; N], ) -> [f64; N]

Advances the state one step under an explicitly supplied control.