On p14 the alternative definition of certainty equivalent states that: cx<0 Why would the certainty equivalent of the gamble alone be negative? Thanks
This is for a risk averse investor with a fair gamble (e.g. equal probability of receiving +1 or -1). A risk averse investor will prefer not to take a fair gamble and will even pay a small premium to avoid the gamble. Therefore cx<0 which is equivalent to paying a small premium to avoid the gamble. This is just the investor accepting less then the expected value (0 in this case) to not take on the gamble's risk.
Because the investor is risk-averse in this instance. So they will pay up to cx to avoid the gamble. But if the investor is risk-loving then cx can indeed become positive i.e. if offered a value of less than cx upfront, they would still gamble.
