NTI is a public institution with the task of insuring key valuables against natural disasters.
NTI is under the auspices of the Ministry of Finance and Economic Affairs and its operations are based on the special Act on Icelandic Natural Disaster Insurance, no. 55/1992.
English translation of the law is available here.
If there is a discrepancy between the English and Icelandic versions, the Icelandic version applies.
The Ministry is responsible for setting the regulation for NTI regarding collection of premiums, damage assessment, determination of compensation and the insured's own risk. Administrative law applies to proceedings at NTÍ. 

The Act on Insurance Contracts No. 30/2004 applies to general criteria for NTÍ's liability, e.g. limitation clauses and interest claims.
The scope of operations varies greatly from year to year, as damage events determine how much manpower is needed at any given time. On average, 4-5 full-time employees work at the Agency, but when larger damage events occur, projects are either shed or people are hired on a temporary basis.