DECISION TREE ANALYSIS
Your organization has enrolled a patient population on a capitation basis. Although some patients will use substantial services and some will use few, the payments your organization will receive will almost certainly cover all the care this population needs if services are managed well, and will result in net earnings for your organization of $1 million after providers and other expenses are paid.
However, there is a 1% chance that one of your enrollees will develop a truly catastrophic condition, resulting in costs of $4 million above and beyond standard costs.
A reinsurance company is willing to sell you an insurance policy that would pay the $4 million excess costs if one of your enrollees develops such a condition. The policy costs $60,000.
Draw a decision tree that indicates, using standard decision tree conventions,
a) Your possible choices
b) Aspects of your situation that are up to chance. Label the chance branches with the probability that they will occur.
c) Label the ends of the branches with the value of each respective outcome.
d) Compute the expected value for the decision branches
e) Do you recommend that your organization buy the insurance? Why or why not?