In this project, we model the cost of fraudulent claims arising over a week from a commercial fire insurance portfolio with an annual gross premium of $1 million. Fraudulent claims may involve arson by the insured or artificially inflated claim amounts.

Question 1 Build and compile an influence diagram in Netica based on the causal structure and probability tables (in percentage values) provided below

, in which Adjuster is a decision variable with possible values of Yes or No.

In the diagram, create a utility node and link "Fraudulent claim", "Fraud detected", and "Cost of fraud" nodes to the utility node. Complete the utility table below based on the following logic:

1. Regardless of the values of "Fraud detected" and "Cost of fraud", if "Fraudulent claim" takes the value of "No", you have the same utility that is equal or higher than that of any other possible outcome in which "Fraudulent claim" takes the value of "Yes".

2. When "Fraudulent claim" takes the value of "Yes", the best scenario is "Fraud detected" takes the value of "Yes" and "Cost of fraud" takes the value of "0". Then, you can imagine that the worst scenario is "no action taken to detect fraud" and "the cost of fraud is higher than 150".

Load the completed utility table into the utility node in the influence diagram.

Save and upload the Netica file containing the complied influence diagram you built.

\begin{tabular}{ccccccc} \begin{tabular}{c} Fraudulent \\ claim \end{tabular} & \begin{tabular}{c} Fraud \\ detected \end{tabular} & \begin{tabular}{c} Cost of \\ fraud \end{tabular} & p. Fraud & p.Detected & p.Cost & U \\ \hline No & Yes & 0 & 1 & N/A & N/A & 1000 \\ No & Yes & 50 & 1 & N/A & N/A & 1000 \\ No & Yes & 100 & 1 & N/A & N/A & 1000 \\ No & Yes & 150 & 1 & N/A & N/A & 1000 \\ No & No & 0 & 1 & N/A & N/A & 1000 \\ No & No & 50 & 1 & N/A & N/A & 1000 \\ No & No & 100 & 1 & N/A & N/A & 1000 \\ No & No & 150 & 1 & N/A & N/A & 1000 \\ Yes & Yes & 0 & N/A & 1 & 1 & 1000 \\ Yes & Yes & 50 & N/A & & & \\ Yes & Yes & 100 & N/A & & & \\ Yes & Yes & 150 & N/A & & & \\ Yes & No & 0 & N/A & & & \\ Yes & No & 50 & N/A & & & \\ Yes & No & 100 & N/A & & & 0 \\ Yes & No & 150 & N/A & & 0 & 0 \end{tabular}