Question: Trailing Stop Loss Distribution

I have done a lot of research and simulation when it comes to trailing stop losses.

I have managed to get very nice results but only through theoretical reasoning

and simulation. However simulation is not as "pure" as manipulating equations.

What I have not managed to do so far is to manipulate the PDF to get an probability

that the trail stop is going to be triggered for a specified normal distribution (mean, volatility)

and trailing distance.

I would assume the problem could be solved by using conditional probabilities.

The intuition is that if we for example set the stop at -10 then we only allow the return to drop -10

for the last n days if it drops more than that the return becomes zero. From a simulation

perspective the price is only allowed to drop -10 from the highest point. The conclusion

is always the same that the expected return remains positive over time and I can prove

this by using a binomial tree but I want to find some elegant mathematical way to

explain this by using conditional density functions.   Any ideas ?!