The distribution of drawdown is highly sensitive to the trading strategy you are running. The distributions of drawdown for a Black Swan strategy and carry strategy are very different. Only you know what you are doing. If you are good, drawdown will have thin upper tail. If you are not good, it may have fat upper tail (or its distribution may fail in other ways). No paper will be able to encompass all the possibilities.
You are on the right track simulating drawdown via Monte Carlo and via backtesting on the historical data.
UPDATE: not only is the assumption of iid Gaussian returns unrealistic; your question is ill-posed for the following reason. The distribution of drawdown can take many shapes depending on the notional rules. The way you
- choose the notional of a new trade,
- readjust the notionals of the open trades
on any given day affects the distribution of the portfolio mark-to-market. Do you ever double down? Do you ever scale down? Are you saying: "If I have 10 trades open already, the 11-th one is not allowed no matter what"? Or are you assuming unlimited balance sheet?
As naive as is, the iid Gaussian framework can be distantly related to returns on a particular asset or static portfolio. However, the framework is completely inapplicable to a portfolio which is rebalanced. Everything depends on how you rebalance. Everything depends on your strategy.