A decision maker is working on a problem that requires her to study the uncertainty surrounding the payoff of an investment. There are three possible levels of payoff -$1,000, $5,000, and $10,000. As a rough approximation, the decision maker believes that each possible payoff is equally likely. But she is not fully comfortable with the assessment that each probability is exactly 1/3, and so would like to conduct a sensitivity analysis. In fact, she believes that each probability could range from 0 to ½.
1. Show how a Monte Carlo simulation could facilitate a sensitivity analysis of the probabilities of the payoff
2. Suppose the decision maker is willing to say that each of the three probabilities could be chosen from a uniform distribution between 0 and 1. Could you incorporate this information into your simulation? If so, how? If not, explain why not, or what additional information you would need
1. For equally likely condition, expected pay-off, E(X) = (-1000+5000+10000)/3 = $4,666.67
An experiment carried out for sensitivity analysis: all three probability values varied randomly between 0 and 1/2 (Montecarlo simulation). Such 100 values generated randomly, their mean values with 95% confidence interval obtained as follows:
mean probability x1 = 0.239 +/- 1.96*0.156/sqrt(100) = [0.209, 0.270]
mean probability ...
Monte Carlo method used for taking some decision, using given data.