In insurance, to determine acceptable risks is the primary responsibility of the:

Answer: Underwriter.

Explanation:

An underwriter is an organization/individual that accesses a risk, and then estimates the cost of the damages resulting from that risk and takes responsibility for the payment of damages, in the eventuality that the risk occurs: The amount paid by the underwriter for a risk, is repaid in the form regular commission by their client.

Therefore the underwriter is primarily the one responsible, for judging if a risk is acceptable to receive payment or not.