1. You can invest in either a mutual fund or a money market fund. In the next year, the mutual fund will increase 20%, increase 10%, not change or decrease 10%. The money market fund will definitely increase by 5%. a. What actions are available to you? b. What states of nature could occur? c. What are the possible outcomes? There is a 10% chance that the mutual fund will increase by 20%. There is a 60% chance the mutual fund will increase by 10%. There is a 20% chance that there will be no change in the mutual fund and there is a 10% chance that the mutual fund will decrease by 10%. In which fund would you invest given each of the below criteria. d. Maximax. c. Maximin. f. Minimax regret. g. First order stochastic dominance. h. The expected value criterion. 2. Repeat question 1 parts (a) - (c) if you have $100 to allocate between the two funds. For instance, you now have the option of investing $25 in the mutual fund and $75 in the money market fund. You could do any other split where you invest a non-negative amount in each fund so that your total investment is $100. 3. Imagine you initially have $5000 of wealth. Consider the problem of choosing an insurance plan. Plan A costs $500 and fully covers all expenses. Plan B costs $100 and covers 80% of your expenses. You also can self insure, that is, you pay no costs up front but you pay the full cost of any incidents. There are four possible states: The probability is 0.1 for a major incident which costs $5000. The probability is 0.3 for a normal incident which costs $1000. The probability is 0.2 for a minor incident which costs $100 and the probability is 0.4 for no incident which does not cost anything. a. Describe the probability distribution of your final wealth under each insurance plan including self insurance. Which insurance plan (or the option to self insure) would you choose under each of the following criteria? b. Maximax. c. Maximin. d. Minimax regret. e. First order stochastic dominance. f. If you maximize the expected value of your final wealth. 4. Prove that it is not possible to choose one lottery under the maximax criterion and another under first order stochastic dominance