I'm working on a project on Importance Sampling. When one tries to estimate the small probability $\alpha:=\mathbb{P}(X \in A)$, one can do a change of measure. There is change of measure which provides an estimate with variance $0$ but of course, this new measure depends on $\alpha$ which we want to estimate. This is thus useless.
I therefore tried the following. I change measure in special way, allowing only a certain kind of measure and optimize the respective paramters. I found 2 possibilites:
1)Exponential change of measure: $d\mathbb{P}/d\tilde{\mathbb{P}} = e^{\theta X}/\mathbb{E}[e^{\theta X}]$.
2) Cross Entropy method: Change to measure in same class and optimize Kullback-Leibler distance.
Are there other changes of measure I should consider?
Thanks in advance, mbktel