1. L(x) = c * x, where c is a "selected link ratio"
2. The value of c is chosen after a review of observed link ratios from previous years
3. The link ratio method fits a line through the origin
4. Optimal method when reported losses are greater than expected and Cov(x,y) > Var(x)
Qualities of Budgeted Loss Method
1. L(x) = k
2. Used if the fluctuation is extreme, or if past data is not available
3. The value of k could be based on variety of data: past loss amounts, earned premium * expected loss ratio, etc.
4. The Budgeted Loss Method fits a horizontal line
5. Also known as "Pegged Loss Method"
6. x and y are totally uncorrelated, i.e., Once k is chosen, y is estimated as k, no matter what x happens to be
7. Optimal method when reported losses are greater than expected and Cov(x,y) < Var(x)
Qualities of Least Squares Method
Credibility Form of Least Squares Method
L(x) = Z * LRE + (1 - Z) * BLE, where
1. LRE = Link Ratio Estimate
2. BLE = Budgeted Loss Estimate
3. Z = b/c
4. c = y/x
2 Adjustments to Losses Before Using Least Squares Development
1. Correction for inflation
2. Divide by exposures
Sampling Errors and Recommended Solutions with Least Squares Method
1. a < 0 implies that the estimate of y will be negative for small values of x. Use link ratio method instead.
2. b < 0 implies that the estimate of y gets smaller as x increases. Use budgeted loss method instead.
2 Situations Where Least Squares Method Can Be Helpful for Developing Losses
1. When developing losses for small states
2. When developing losses for lines that are subject to serious fluctuations
Advantages of Using Best Linear Approximation of Bayesian Estimate
In comparison to the actual Bayesian estimate, the best linear approximation is:
1. Simpler to compute
2. Easier to understand and explain
3. Less dependent upon the underlying distributions
Relationship of Cov(X,Y) and Var(X)
1. If Cov(X,Y) < Var(X), a large reported amount should lead to a decrease in the reserve
2. If Cov(X,Y) = Var(X), a change in the reported amount should not affect the reserve
3. If Cov(X,Y) > Var(X), a large reported amount should lead to an increase in the reserve
Enterprise Risk Management
Definition: Discipline by which an organization in any industry assesses, controls, exploits, finances, and monitors risks from all sources for the purposes of increasing the organization's short-and long-term value to its stakeholders