Mathematical Finance
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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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