Imagine that you have $5,000 to invest and that you will an opportunity to inves
ID: 3267185 • Letter: I
Question
Imagine that you have $5,000 to invest and that you will an opportunity to invest that amount in either of two investments (A or B) at the beginning of each of the next 3 years. Both investments have uncertain returns. For investment A you will either lose your money entirely or (with higher probability) get back $10,000 (a profit of $5,000) at the end of the year. For investment B you will get back either just your $5,000 or (with low probability) $10,000 at the end of the year. The probabilities for these events are as follows: You are allowed to make only (at most) one investment each year, and you can invest only $5,000 each time. (Any additional money accumulated is left idle.) (a) Use dynamic programming to find the investment policy that maximizes the expected amount of money you will have after 3 years. (b) Use dynamic programming to find the investment policy that maximizes the probability that you will have at least $10,000 after 3 years.Explanation / Answer
E(X) for A = 0.3 + 0.7(10000) = $ 7000
E(X) for B = 0.9(5000) + 0.1 (10000) = $5500
So, clearly, A is a better investment, & after three years, the expected amount of money is 7000*3 =$21000
The investment policy that maximizes the probability of having at least $10000 after three years, is to invest in A throughout the years.
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