Give the von Neumann-Morgenstern utility function. A utility function has expected utility propety if u(g)=∑p_{i}u(a_{i}) for any g∈G where (p₁°a₁,...,p_{n}°a_{n}) is the simple gamble induced by g. The von Neumann-Morgenstern utility function is typically denoted as � ( � ) U ( x ) , where � x represents an outcome or a set of outcomes. This utility function satisfies the expected utility property, which states that for any gamble � g with associated probabilities � � p i and outcomes � � a i , the utility of the gamble � ( � ) u ( g ) is equal to the sum of the probabilities weighted by the utility of each outcome: � ( � ) = ∑ � � � ⋅ � ( � � ) u ( g ) = ∑ i p i ⋅ u ( a i ) Here: � ( � ) u ( g ) represents the utility of the gamble � g . � � p i is the probability associated with the outcome � � a i . � ( � � ) u ( a i ) is the utility of the outcome � � a i . The sum is taken over all possible outcomes of the gamble. This property essentially captures ...
Life income joint and survivor settlement option guarantees a) Income for 2 or more recipients until they die. b) Payment of interest on death proceeds. c) Payout of the entire death benefit. d) Equal payments to all recipients. Answer: a) Income for 2 or more recipients until they die.