Struct Merton 

pub struct Merton {
    pub risk_free_rate: f64,
    pub mu: f64,
    pub sigma: f64,
}

Merton log-utility portfolio problem.

See the module-level documentation for the formulation and exact solution.

Fields

risk_free_rate: f64

Risk-free rate.

mu: f64

Risky-asset drift.

sigma: f64

Risky-asset volatility.

Implementations

impl Merton

pub fn new(risk_free_rate: f64, mu: f64, sigma: f64) -> Self

Creates a Merton problem.

Panics

Panics if sigma is not positive.

Examples

use solver::models::merton::Merton;
let m = Merton::new(0.03, 0.08, 0.2);
assert!((m.sigma - 0.2).abs() < 1e-12);

pub fn exact_policy(&self) -> f64

Optimal (constant) portfolio fraction.

Examples

use solver::models::merton::Merton;
let m = Merton::new(0.03, 0.08, 0.2);
assert!((m.exact_policy() - 0.05 / 0.04).abs() < 1e-12);

pub fn exact_value(&self, wealth: f64, tau: f64) -> f64

Closed-form value function V(t, x) for remaining horizon tau = T - t.

Examples

use solver::models::merton::Merton;
let m = Merton::new(0.03, 0.08, 0.2);
let v = m.exact_value(100.0, 1.0);
assert!(v.is_finite());

Trait Implementations

impl Clone for Merton

fn clone(&self) -> Merton

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ControlProblem<1> for Merton

type Control = f64

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; 1], _derivs: &StateDerivatives<1>, ) -> Self::Control

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

fn running_reward( &self, _t: f64, _state: &[f64; 1], _control: &Self::Control, ) -> f64

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

fn generator( &self, _t: f64, state: &[f64; 1], control: &Self::Control, derivs: &StateDerivatives<1>, ) -> f64

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

fn terminal(&self, state: &[f64; 1]) -> f64

Terminal value g(x) at the horizon.

fn next_step( &self, _t: f64, state: &[f64; 1], dt: f64, noise: &[f64; 1], ) -> [f64; 1]

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

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

Whether a dimension is driven by Brownian diffusion.

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 bsde_driver( &self, t: f64, state: &[f64; N], control: &Self::Control, _derivs: &StateDerivatives<N>, _dt: f64, ) -> f64

Returns the backward driver consumed by the BSDE regression solver.

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 discount_rate(&self, _state: &[f64; N]) -> 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_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.

fn is_reduced_value(&self) -> bool

Whether the value this problem solves is a reduced value.

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

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

impl Copy for Merton

impl Debug for Merton

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl From<&MertonJump> for Merton

The no-jump reduction of MertonJump with jump_rate = 0.

fn from(model: &MertonJump) -> Self

Converts to this type from the input type.

impl PdeProblem<1> for Merton

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

Discretization kind for dim.

fn transport( &self, _t: f64, state: &[f64; 1], control: &Self::Control, _derivs: &StateDerivatives<1>, ) -> Transport<1>

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.