Thank you for question, Mattia.
Usually these words are associated with verbs.
Prize = to win; something (a gift) that is won by some contest or competition
Award = to give; something (a gift, recognition) that is given to someone
Premium = to pay, to receive, to earn, to cost
In the United States, "premium" can have an exact legal definition.
In most cases a premium is paid to someone or received, depending on the context.
Premiums are sums paid to meet some legal requirement or exchange for service, or as in
insurance schemes: what is paid to receive insurance coverage.