AgentSkillsCN

stochastic-calculus-sde

在量化金融领域，用于数值模拟随机微分方程、离散化误差分析以及路径统计的流程。当任务涉及伊藤过程的模拟与数值方案的验证时，可予以采用。

SKILL.md
--- frontmatter
name: stochastic-calculus-sde
description: "Stochastic differential equation workflows for numerical SDE simulation, discretization-error analysis, and pathwise statistics in quantitative finance. use when tasks involve simulating Ito processes and validating numerical schemes."

Stochastic Calculus SDE

objective

Simulate and validate SDE dynamics with controlled numerical error and path diagnostics.

workflow

  1. •define drift and diffusion specifications for target process.
  2. •implement Euler, Milstein, or higher-order discretization schemes.
  3. •quantify discretization bias and variance across step sizes.
  4. •validate path statistics against analytical moments when available.
  5. •promote simulation settings only after convergence diagnostics pass.

required diagnostics

  • •strong and weak convergence versus time-step size.
  • •pathwise moment and autocorrelation consistency checks.
  • •stability under volatility and drift regime shifts.
  • •random-seed sensitivity and reproducibility diagnostics.
  • •tail-path behavior under extreme shocks.

risk controls

  • •enforce minimum convergence standards before use.
  • •enforce deterministic seed management in research pipelines.
  • •enforce fallback discretization when instability appears.

outputs

  • •run python scripts/stochastic_calculus_sde_diagnostics.py input.csv --output diagnostics.json and keep the json artifact.
  • •write an implementation memo using references/stochastic-calculus-sde-playbook.md with assumptions, tests, limits, and rollout plan.

resources

  • •use scripts/stochastic_calculus_sde_diagnostics.py for deterministic diagnostics.
  • •use references/stochastic-calculus-sde-playbook.md for the domain checklist and delivery structure.