Courses Stochastic Calculus for Finance Proof Gym
Proof Gym
The proofs this course leans on, in the same four formats as the Foundations Proof Gym. Probability inequalities first, then reading and writing proofs about conditional expectation and martingales.
- 2 stages
- About 6 hours
- Alongside Foundations Level 5 and Parts 1–2
PG7 · Probability inequalities
Markov, Chebyshev, Jensen, Cauchy–Schwarz. Worked example: The weak law of large numbers from Chebyshev.Lessons coming soon.
PG8 · Probability proofs
Reading textbook proofs, Conditional-expectation arguments, Martingale arguments. Worked example: The tower property; W² − t is a martingale.Lessons coming soon.
Every proof starts with the numbers
A lesson first checks the claim in Python, then states it, then proves it in up to four formats, easiest first.
1. Reorder the steps
The lines of a proof, shuffled. Put them back in order, with the arrows or by dragging.
2. Fill the gap
A proof with its key steps missing. Supply each one, checked like a quick answer.
3. Find the error
A proof that looks right but is not. Pick the faulty line and say what is wrong.
4. Write it
Write the proof yourself, then compare it with a model answer and a checklist.