Maths in economics, finance and society · Solid · Dissertation

The Kelly criterion: how much to risk: a maths EPQ idea

Why it works as an EPQ

Logarithms and calculus give a clear optimum, and simulations show its risks.

Scope and difficulty

Solid. Solid. Simple repeated bets; no gambling as part of the project.

The maths

Builds on these A Level topics: Exponentials and logarithms · Differentiation · Probability.

You would learn:

• Expected log growth
• Optimising with calculus
• Volatility of outcomes

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Derive the Kelly fraction for a simple repeated bet.
2. Simulate wealth paths for different fractions.
3. Compare growth with the chance of large losses.
4. Judge why many people use a fraction of Kelly.

Pitfalls

• Presenting it as betting advice.
• Using expected wealth rather than expected log wealth.

Where to start reading

• Search for: Kelly criterion derivation log utility
• Fortune's Formula (William Poundstone)

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All maths in economics, finance and society ideas · all 93 ideas

Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.