Thank you for your question, and thanks for using JustAnswer. Happy New Years! Your issue is handled under the Constructive Receipts doctrine, which states "You have constructive receipt of income when an amount is credited to your account or made available to you without restriction. You do not need to have possession of it. If you authorize someone to be your agent and receive income for you, you are treated as having received it when your agent received it." SOURCE
So, since your broker is your agent, and they received the payment on December 31, you also received the payment on December 31. So, they are correct in issuing your check dated December 31 and issuing you a 1099 for 2012.
It's not when you get the check, it's when it's made available to you. I know you could argue that you didn't get the check until today, but your agency (the broker) did get receipt on the 31, and therefore you are presumed as getting the check on that same day as well.
I hope this makes sense. Please follow up with me if you need anything additional. Have a happy New Years and thanks again for coming to our site and using our service.
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You should be aware that your question, as with most tax questions, can never really be answered completely...addressing all the permutations; that is because of the many assumptions that have to be made I have done my best to determine what I think you are asking and answering it in the most direct and understandable manner possible. If, however, after reviewing the questions, you have any uncertainties or further questions, please do not hesitate to ask.