No amortization problem, it follows the ownership/stock sale, just like your house or your car, a gallon of gasoline, or anything else you buy/sell. So when you sell your stock the embedded value/energy goes with it. If you received dividends, and spent it then that probably had some embedded energy too. If you have money in the bank, then that earns interest which you'll spend/save, and if you own Gov bonds then you own part of the government, which has spent lots directly on concrete and oil. None of that concrete is free (you could argue they should get credits for all the un-cut trees grown on federal land though).
Even donations to charity have carbon footprint. Imagine you give to a charity that pays gas bills for poor people. Those people didn't buy that oil/gas. The one giving to charity did.
You earn money, you spend money, you save money, you give away money... that money gets spent on objects with embedded carbon. Unless you want to say that corporations get a free pass, or the government gets a free pass, or banks get a free pass, or wealthy people get a free pass. Just like taxes... maybe the monarchy gets a free pass?
Now there's still a way to game it, which is to have your company pay for everything. Just like cheating on your taxes, if you have no income and everything is held in a corp, then whoever holds the corp owns your carbon production.