# Tag Info

This is what I would do without access to pen and paper. I don't know whether this strategy is optimal but it is easy to execute and I invite others to do better :) The problem in this setup is that I don't know my probability of winning as $x$ and $y$ are unknown and I can't apply the Kelly criterion. To wit (Wikipedia): Where losing the bet involves ...
In this case, you could consider the quadratic variation of the asset price paths to indicate trading range. By quadratic variation, I make reference to the mathematics used in Stochastic Calculus, which is compute path-by-path (Steven E. Shreve, 2008). $[M,M]_k=\sum^{k}_{j=1}{(M_j-M_{j-1})^2}$ Using your example above, Asset A variation is calculated as ...