This note tries to correct a deficiency of the microeconomic literature on decision making under uncertainty. Indeed, when considering meaningful comparative statics results in situations where risks are at least partially controllable (endogenous), this literature has mostly relied upon the traditional Arrow-Pratt risk aversion functions and has paid very little attention to the definition of the risk premium. However when they defined the risk premium and the risk aversion functions, Arrow and Pratt considered only roulette gambles, i.e. risks totally exogenous to the individual. This note highlights the fact that several definitions of the risk premium may be proposed for endogenous risks. Two of them, already used in the literature, do not preserve the intuitively-appealing properties of the Arrow-Pratt risk premium. An alternative definition is then proposed. It is shown that this new definition of the risk premium applied to endogenous risks exhibits the properties generally admitted for roulette gambles.