The Minister of Finance was a government official on Barrayar and in the Barrayaran Imperium. It seems plausible that his duties would include collecting taxes for the Emperor's government. Imperial Auditor Vorhovis served as Assistant Minister of Finance before he was appointed as an Auditor.
The Minister of Finance likely did more than collecting taxes, as given real world equivalents of this role, he would probably have been the chief economic officer for the Barrayaran Imperium. Thus, his duties may have included taking leading roles in trade, commerce, the budget, monetary policy, and possible treaty negotiations.
- Memory, chapter 28