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Qualities of Link Ratio Method
- 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