two questions
- Is it important to define your edge mathematically?
- How do you go about trying to find an edge?
Unless it is some risk free arb, but most trading edges cant be mathematically proven like a roulette wheel.
You can find an edge by backtesting a strategy. However there is no certainty the edge will hold up going forward. We just hope it will hold up.
You have try to lots of strategies, many will look promising, but most will fail when forward tested. If you are lucky you might find an edge that continues to work in forward trading for many years. And bet big while the sun shines.
.