Imagine that you have $5,000 to invest and that you will an opportunity to inves

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

Expected return per year, E(X=A) in Investment A = 0.3*0 + 0.7*10000 = $7000

Three year return with confidence = 7000*3 =21000

Expected return per year, E(X=B) in Investment B= 0.9*5000 + 0.1*10000 = $5500

Three year return with confidence = 7000*3 =$21000

Part A

The policy should be to incest only in investment A for three consecutive years.

Part B

Even to maximize the confidence that you will have at least $10000 after three years , Investment A should be selected, with expected additional benefit = (7000-5500)*3 = $4500

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