Avoid exponential overflow in entropic risk calculations - #270

I checked the new formula against the old one outside the library (numpy and scipy, same expressions as the diff, a shaped (T, 1) like the .item() path expects):

So the two agree to the last digit or two where the old one is finite, and the new one stays finite where np.exp(-a / z) overflows. The old version breaks once -a / z exceeds about 709.78, i.e. any return below -709.78 * z: with z = 0.001 a constant -0.7 is still finite and -0.8 gives inf, which is why the -0.5/-0.7/-0.8 boundary shows up so soon at small z. That matters for _Entropic_RM(z, X, alpha) because z is the variable minimize searches over, so the optimiser can step to a small z where the old objective returned inf or nan.

One edge I would add a test for: a zero-row input. logsumexp of an empty axis is -inf and np.log(0) is -inf, so the new expression returns nan (I ran it); it is also nan on the old path, so this is not a regression, but the raise-on-non-finite check above it could cover len(a) == 0 explicitly.

Hi @galafis,

I am going to reject this pull request, as all the errors occur in scenarios that are not realistic. It is actually a good thing that the function failed when faced with a returns vector that do not correspond to reality. If there is a 100% loss (Not possible in finance), all returns are the same, or a sample is too small, the problem is the data. Please read about financial theory before submitting a pull request.

Best,
Dany