2026 · July

Level 9:

Option Pricing and exact solutions

• exact solutions for perpetual American options
• Affine interest rate models (interest rate derivatives)
  • Stochastic differential equations (with brownian motion)

get it working:

• Clewlow
• Strickland
  get it right:
• adaptable
• Kienitz/Duffy
  get it optimized:
• Monte Carlo Engines

Monte Carlo Simulations

• easy to program and always get an answer, we simulate many paths and take the average

FDA (Finite Difference Approximation)

• Euler (Explicite and Implicite)
• Milstein (Ito)
• Runge-Kutta

Finite Difference Methods

Lattice methods

• Binomial methods

Setup

• warm water
• lean over the sink and keep your lips mostly closed to reduce splashing
• its ok for it to be a bit messy

Start

• use it before brushing if you want to flush debris out first
• start with lower pressure and gradually increase the pressure until comfortable

Technique

• aim at the gum line
• go tooth to tooth and pause briefly instead of sweeping too fast
• slow down more for the back teeth

Aftercare

• if gums bleed at first, keep the pressure gentle and see if it improves over several days
• clean the device regularly, especially the tip and reservoir

Started growth.jonasruilong.com as the personal growth hub so I remember what I have done and learned so I dont make the same mistakes again :(

• a timeline of dated snapshots, living threads that deepen over time, plus mission, books, and relationship.

• File-based markdown in git; visibility so some entries stay private or title-only
• Snapshots can open into a thread (or point at an edu note)
• Shared login when viewing protected entries

Achievements:

• Growth site live with the content model in active use
• Snapshots, threads, mission, books, and relationship areas wired together