Optimisation and game theory · Maths EE idea · Ambitious

How much to bet: the Kelly criterion

A research question to start from

Why does betting a fixed fraction given by the Kelly criterion maximise long-run growth, and what are the risks of betting more?

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Why it works as a maths EE

Logarithms and expectation in an optimisation with a sharp conclusion.

Mathematics you would need

Expected logarithmic growth
Optimisation with calculus
Law of large numbers (informally)
Simulation

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Derive the Kelly fraction.
Show over-betting reduces growth and analyse ruin risk.
Simulate and discuss assumptions.

Scope and difficulty

Ambitious. Ambitious; keep it about mathematics, not gambling advice.

Pitfalls

Promoting betting.
Expected value confused with growth rate.

Where to start reading

Search a library catalogue or a university's open lecture notes for: Kelly criterion derivation log utility; over-betting growth rate. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

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