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The company has promised its clients unrealistically high yields and a guarantee on principal.
The MNB has launched the investigation to establish whether the company collects deposits or other financial assets on a business basis, something that requires permission from the MNB under the law.
The MNB has also filed a criminal complaint on the matter.
Goldsten Limited has no licence to perform such activities in Hungary.
The MNB said it had already issued a warning earlier to consumers on the matter.