Mathematical Finance
The Man Who Could Have Won the Nobel Twice
In 1965 Paul Samuelson wrote down an option formula with two unknowns, and admitted he had no theory to pin them down. Set both to the interest rate and it is the Black–Scholes–Merton formula, term for term, eight years early. The missing piece was not mathematics but an argument, and his own student helped supply it.
Read more →Kelly, the Growth-Optimal Portfolio, and the Benchmark Approach to Option Pricing
The Kelly criterion and Black-Scholes option pricing are the same mathematical object viewed from different angles. Both lead to the growth-optimal portfolio — Platen's benchmark — which prices derivatives under the real-world measure without requiring a risk-neutral one.
Read more →CAD 530 a Month: What Your Car Insurance Premium Actually Pays For
A friend bought a Ford F-150 in Ontario. The insurance quote came in at 530 dollars a month. I built a mathematical model to find out how much of that is justified.
Read more →Langevin Dynamics and Why They Matter in Finance
The Langevin equation was written to describe a particle in a fluid. It turns out to be exactly the right language for interest rates, volatility, and forward curves.
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