Limiting conditions, conditions, conditions, my friend. Otherwise nobody would be working on improving VWAP trading engines. You are basically asking for the holy grail. Its like me asking you how I should structure a vwap trading strategy: Should I buy the full size of the order if price drops intraday beyond 2 standard deviations or 3 or 4...10? If not full size, how much. In order to even start answering the question you need to introduce boundary conditions.

I think a good way to think about your problem is the example of finding an optimal VWAP trading strategy. You basically have a finite point in time by which you must have performed your transaction and you trade a similar asset than the one you are considering, one with the same underlying assumptions of mean-reversion (I make such assumption in the same way than you make the assumption of mean-reversion).

With this assumption in mind and given you must at some point in time transact you are now faced with the following optimization problem: By how much does the asset have to traverse away from whatever you define as mean point in order to induce you to transact and in what size?

Also, contrary to a pairs trading strategy you do not want to transact at the point where an asset moved away from its mean but in the same direction as your order direction. You believe in mean-reversion and assume you can transact the asset more optimally at a later point.

I cannot provide an optimization function (because its very closely related to something I have been working on in the past and do not want to make it public) but here couple points I would consider:

• Does the asset really mean-revert more often than it trends in order to overcome each and every cost of execution, including commission, market impact,...? Does it pay to consider implementing a hybrid strategy in which you measure regime changes and only employ a mean-reversion approach when price dynamics favor such approach?
• Get a firm grasp at how volatile the asset is. By how many standard deviations does the asset trade away from its mean?
• Are you willing to take on more proprietary risk in that you are willing to potentially transact the full size of your order at once given the asset diverted sufficiently much away from your defined mean? Or do you want to split the order into many child orders and trade smaller sizes at smaller diversions?

I would first try to answer and consider those points before proceeding. Please note I am sharing my own experience here and do not present an academic approach. I implemented a VWAP strategy with systematic proprietary overlay that performed at a close to zero tracking error over a longer period of time in several Asian equity markets, including names that were generally not considered to be executed through standard DMA engines either for lack of liquidity, or other anomalies.