Exam 6: Decision Making Under Uncertainty

The expected value of sample information (EVSI)is the difference between the EMV we can obtain with sample information and the EMV we can obtain without information.

In decision trees,a decision node (a square)is a time when the result of an uncertain event becomes known.

(A)Construct a decision tree to help the company make its decision.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities. (B)What is the best lease option? Why? (C)Suppose the company could hire an experienced mechanic to inspect the old grader to determine the repair cost before the company makes its final decision.If the mechanic is always correct in his assessments,what is the most the company would pay for the inspection?

Expected monetary value (EMV)is:

Which of the following can be obtained with a tornado chart?

A risk profile lists all possible monetary values and their corresponding probabilities.

(A)Construct a decision tree to help the investor make his decision.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities. (B)What is the best choice for the investor? Why? (C)Suppose that investor has an exponential utility function for final assets with a risk tolerance parameter equal to $60,000.Which investment opportunity will he prefer in this case? What is his certainty equivalent?

Construct a decision tree to help Mrs.Rich decide whether or not to purchase insurance.Note that the tree should minimize Mrs.Rich's annual expected total cost,including the possible insurance premium,deductible payment,and damage payment.In your tree,make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.

One class of "ready-made" utility functions is called exponential utility.Exponential utility has an adjustable parameter called risk tolerance.The risk tolerance parameter measures:

For a risk averse decision maker,the certainty equivalent is less than the expected monetary value (EMV).

Perform a sensitivity analysis on the optimal decision and summarize your findings.Vary the probability of being in an accident from 0% to 10%,the insurance premium from $50 to $300,and the deductible amount from $0 to $600.In response to which model inputs is the expected total cost value most sensitive?

As the average monthly revenue associated with the rock format and an A1 audience varies between about $142,500 and $200,000,what happens to the maximum expected revenue? Briefly explain why.

If x is a monetary value (a payoff if positive,a cost if negative),U(x)the utility of this value,and R > 0 is an adjustable parameter called the risk tolerance,then the function U(x)= 1 - is called

There are three types of nodes that are used with the decision trees.They are the:

The certainty equivalent is the certain dollar amount a risk-averse decision maker would accept in order to avoid a gamble altogether.

Should Southport conduct the imperfect core test if it costs $250,000?

(A)Construct a decision tree to help the power company decide what to do.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities. (B)Where should the power company build the plant? What is the expected cost? (C)Suppose that a geologist (and his team)can be hired to analyze the fault structure at Chico Canyon.He will either predict whether an earthquake will occur or not.If the geologist is perfectly reliable,what is the most the company should be willing to pay for his services? (D)Suppose that an actual (not perfectly reliable)geologist can be hired to analyze the earthquake risk.The geologist's past record indicates that he will predict an earthquake on 90% of the occasions for which an earthquake will occur and no earthquake on 85% of the occasions for which an earthquake will not occur.Given this information,what are the posterior probabilities that an earthquake will and will not occur,given the geologists predictions? (E)Should the company hire the geologist if his fee is $1.5M?

Decision trees are composed of nodes (circles,squares,and triangles)and branches (lines).

Is this decision maker risk averse? Explain why or why not.

What should the network do? What is their expected profit?