Attitude towards Risk:
Let's assume the following: The utility function
• has the single argument "wealth" measured in monetary units,
• is strictly increasing, and
• is continuous with continuous first order and second order derivatives.
The expected value of the lottery (P, W1, W2), where the Wi are the different wealth levels, is the sum of the outcomes, each multiplied by its probability of occurrence. Thus,
E [W] = PW1 + (1-P)W2
A person is risk neutral relative to a lottery if its utility of the expected value equals the expected utility of the lottery, i.e., if
U [PW1 + (1-P)W2] = PU (W1) + (1-P)U(W2) ---------------- (a)
Such a person is only interested in expected values and is totally oblivious to risk. If she is risk neutral towards all lotteries, equation (a) implies that she has a linear utility function of the form U = α + βW with β>0. The utility analysis developed for certain situations is applicable for risk-neutral persons facing uncertainty. All that is necessary is to replace certain values with expected values. A person is a risk averter relative to a lottery if the utility of its expected value is greater than the expected value of its utility:
U [PW1 + (1-P)W2] > PU (W1) + (1-P)U(W2) -------------- (b)
Such a person prefers a certain outcome to an uncertain one with the same expected value. If equation (b) holds for all 01 and W2 within the domain of the utility function, the utility function is strictly concave over its domain since equation (b) is identical to the definition of strict concavity.