72 lines
1.9 KiB
Rust
72 lines
1.9 KiB
Rust
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//! Optimal Control Module
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//! ======================
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//!
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//! Generic optimal control algorithms for dynamical systems.
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//!
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//! # Features
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//!
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//! - Generic HJB PDE solver with finite differences
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//! - Viscosity solutions for non-smooth value functions
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//! - Upwind schemes for numerical stability
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//! - Parallel processing support
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//!
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//! # Mathematical Foundation
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//!
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//! ## Hamilton-Jacobi-Bellman Equation
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//!
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//! For a general stochastic process dX_t = μ(X_t)dt + σ(X_t)dW_t,
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//! the HJB equation is:
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//!
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//! ρV(x) = sup_u [μ(x,u)V'(x) + (σ²(x,u)/2)V''(x) + L(x,u)]
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//!
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//! where:
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//! - V(x) is the value function
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//! - ρ is the discount rate
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//! - u is the control
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//! - L(x,u) is the running cost
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//!
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//! ## Viscosity Solutions
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//!
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//! Handle non-smooth value functions via:
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//! 1. Finite difference discretization
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//! 2. Upwind schemes for stability
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//! 3. Iterative convergence to viscosity solution
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pub mod hjb_solver;
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pub mod jump_diffusion;
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pub mod mrsjd;
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pub mod regime_switching;
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pub mod viscosity;
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pub use hjb_solver::{HJBConfig, HJBResult, HJBSolver};
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pub use jump_diffusion::{
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JumpDiffusionConfig, JumpDiffusionResult, JumpDiffusionSolver, JumpDistribution,
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};
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pub use mrsjd::{MRSJDConfig, MRSJDResult, MRSJDSolver, RegimeJumpParameters};
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pub use regime_switching::{
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RegimeParameters, RegimeSwitchingConfig, RegimeSwitchingResult, RegimeSwitchingSolver,
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};
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pub use viscosity::{ViscosityConfig, ViscositySolver};
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use thiserror::Error;
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#[derive(Error, Debug)]
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pub enum OptimalControlError {
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#[error("Numerical error: {0}")]
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NumericalError(String),
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#[error("Convergence failed: {0}")]
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ConvergenceError(String),
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#[error("Invalid parameters: {0}")]
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InvalidParameters(String),
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#[error("Insufficient data: need at least {0} points")]
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InsufficientData(usize),
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#[error("Matrix computation error: {0}")]
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MatrixError(String),
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}
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pub type Result<T> = std::result::Result<T, OptimalControlError>;
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