Suppose the management of a firm is trying to allocate liquid assets to two accounts, one of which is riskless but pays no interest, while the other offers a risky return. Assume the rate of return r on the second account is uniformly distributed over the range [-0.5, 0.5]. Let R denote the amount currently available for allocation to the two accounts, and S denote the amount invested in the risky asset.
Suppose management would like to make the next period investment value as large as possible but subject to the condition that R + Sr not fall below 95% of the original value of R too often so that if the investment falls below 95% of its original value, it should not do so more than 25% of the time.
Calculate the ratio of investment and the amount available, that is, a = S/R
