= = a 1. Consider a risk-averse decision maker (DM) whose initial wealth is $1000 facing the risk of losing $400 with probability p = 0.05. Assume that the decision maker's utility function is u(w) = ln w, where w denotes the DM's level of wealth. Suppose that the DM is offered insurance against this loss. Let the insurance premium, a, be determined according to the formula: a = 1.1pp/(1 p) where denotes the net indemnity payment in case of a loss and the loading factor is 1.1. (a) What is the optimal insurance policy (a*, *) of this decision maker? (b) What is the minimum deductible under the optimal policy? (c) What will be the effect on the optimal level of coverage, *, of an increase in the level of potential loss, from $400 to $500? (d) What will be the effect on the optimal level of coverage, *, of an increase in the probability of loss to p = 0.1? (d) Suppose that the DM is offered fair insurance. What will be the effect of an increase in the probability of losing $400 on the optimal level of insurance coverage? (e) Consider a decision maker whose utility function is v (w) = ln w2 whose initial wealth is $1000 facing the risk. What is the optimal insurance policy of this decision maker? How does it compare to that of the first decision maker? Explain your result (hint: go back and look at the expected utility theorem). = = = = a 1. Consider a risk-averse decision maker (DM) whose initial wealth is $1000 facing the risk of losing $400 with probability p = 0.05. Assume that the decision maker's utility function is u(w) = ln w, where w denotes the DM's level of wealth. Suppose that the DM is offered insurance against this loss. Let the insurance premium, a, be determined according to the formula: a = 1.1pp/(1 p) where denotes the net indemnity payment in case of a loss and the loading factor is 1.1. (a) What is the optimal insurance policy (a*, *) of this decision maker? (b) What is the minimum deductible under the optimal policy? (c) What will be the effect on the optimal level of coverage, *, of an increase in the level of potential loss, from $400 to $500? (d) What will be the effect on the optimal level of coverage, *, of an increase in the probability of loss to p = 0.1? (d) Suppose that the DM is offered fair insurance. What will be the effect of an increase in the probability of losing $400 on the optimal level of insurance coverage? (e) Consider a decision maker whose utility function is v (w) = ln w2 whose initial wealth is $1000 facing the risk. What is the optimal insurance policy of this decision maker? How does it compare to that of the first decision maker? Explain your result (hint: go back and look at the expected utility theorem). = =