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# Monte Carlo Simulation and Sensitivity Analysis

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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

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#### Solution Preview

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 ...

#### Solution Summary

Monte Carlo method used for taking some decision, using given data.

\$2.49