The Tweedie model also allows for heteroscedasticity - as with gamma, the variance is a function of the mean. It is a compound model combining Poisson and gamma - see the "Details: Tweedie Distribution for Generalized Linear Models" section of the GENMOD documentation. Also, the compound model fit by PROC HPCDM *is* a two-part model for frequency of loss and severity of loss - the frequency model can be Poisson, negative binomial, or zero-inflated model, and the loss model is automatically selected as the best fitting among many continuous distributions including gamma and others. See the Getting Started example in the PROC HPCDM documentation.
The paper you refer to doesn't seem to suggest a specific model. It suggests first fitting a logit or probit model to the binary response of zero or positive cost, and a GLM based on a chosen distribution on the positive cost responses. The logit or probit binary response, first part model can be fit in PROC LOGISTIC or PROC GENMOD. The GLM second part, continuous response model can be fit using PROC GENMOD. PROC SEVERITY in SAS/ETS can automatically select the best distribution (as is done with HPCDM). The ASSESS statement in GENMOD allows for testing the adequacy of the link function and the specified form of the model.
For count responses, it mentions the two-part hurdle model which can be fit with PROC FMM (see this note). A similar two-part count model is the zero-inflated model which can also be fit in FMM (see "Getting Started: Modeling Zero-Inflation" in the FMM documentation) and in PROC GENMOD and PROC GAMPL. See the "Details: Zero-inflated models" section in the GENMOD documentation. FMM could be used in a similar way, as shown for the hurdle and zero-inflated models, to fit a zero-inflated gamma model.
