Hi guys,
I agree with Philip that the original version sounds odd.
Let's say our friend Tom decides to fight a duel with pistols.
Whether or not he thinks he will win, wouldn't you say that he is willing to risk dying, rather than that he is willing to risk living?
The relevant entry in my dictionary defines
the noun risk as 'chance or possibility of danger, loss, injury or other
adverse consequences' (the pink italics are mine)
and
the verb risk as 'expose to risk, accept the chance of risk'.
Best wishes, Clive