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, W_{1}, W_{2}), where the Wi are the different wealth levels, is the sum of the outcomes, each multiplied by its probability of occurrence. Thus,
E [W] = PW_{1} + (1-P)W_{2}
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 [PW_{1} + (1-P)W_{2}] = PU (W_{1}) + (1-P)U(W_{2}) ---------------- (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 [PW_{1} + (1-P)W_{2}] > PU (W_{1}) + (1-P)U(W_{2}) -------------- (b)
Such a person prefers a certain outcome to an uncertain one with the same expected value. If equation (b) holds for all 0
1 and W_{2} 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.