Which model of survival analysis?

Hi guys,

in my thesis I am looking at determinants of exit strategies for businesses. In particular, I want to see whether governance related variables such as the generation in control influence the probability for three different exit strategies. Now, I am puzzled by what exact model to use.
The exit event is recorded in yearly intervals, so I assume I need to use a model for discrete data. However, I did find some papers that used the cox proportional hazard model, which was originally developed for continuous data - right?
Additionally, the three different exits are "competing risks", meaning that firms are excluded from the sample after they have followed one of the exit strategies, so a firm cannot at the same time follow two of the exit strategies.
After searching the web and reading papers, my best bet at the moment is to use a cloglog model. However, I am uncertain whether this is the right approach for my data, given that I look at competing risks and not at a binary dependent variable, but at a categorical with three possible outcomes. Another approach I have seen in papers is to split up the groups and change the dependent variable into binary ones (Exit Strateg 1: Yes/No, etc.) and one pooled exit (Exit: Yes/No).

I appreciate any help very much as I do not know how to go from here.

Best wishes,