# Position sizing for a mean reversion strategy

I have a model that returns z scores for a mean reversion strategy where z score is the current price minus average and divided by vol.

At the moment, positions are sized inverse linear to the z score as mentioned in many forums and Ernie Chan's book.

I tried to improve by using squared and cubic measures of the z score and realized that there could a mathematical way to optimize this and identify the optimal sizing given z scores. Does something like that exist? Tried searching for research papers on this but did not find any.