The responsibility of the broker is to put your limit order out in the marketplace. Other than routing the order to the exchange, they don't actively buy the stock on your behalf and, even if they did, they would never buy it higher than your limit price, even if it is a fraction of a cent. Once your order is out there, you need someone else to sell at your limit price and at the exchange/venue your stock is listed at. Thus, I can guarantee that if the stock trades above your limit, you will not get executed. Even if it trades at your limit, you may not get executed. Your order may be behind someone else's at that venue or the stock may trade on a different venue from where you order is located.
Actually, even if trades below your limit, it may not get executed. Although that is not supposed to happen, it does on occasion, particularly if your order is not routed to the NYSE and you miss the opening/closing auction prices.
MC |