BAIC 3 - Ratemaking Procedures and Concepts Flashcards
What is the single most important objective with any business?
Income >=Payments
What makes up insurance income?
Premium - amount insured pays to be covered
Investment Income - interest earned on money that has been paid to the company but not yet been paid out as losses; Most important in lines of business with long periods of time between when the premium is received and when claims are paid
Rate vs. Loss Cost
Rate - actual amount that an insurer would charge an insured for coverage, expressed as a per-exposure measure
Loss cost - estimate of future loss payments, including such costs as claims handling and legal defense. The portion of the rate that covers expected losses and loss adjustment expenses
Ratemaking Methods
Pure Premium
Loss Ratio
Judgmental
Modeling
Fundamental ratemaking equation used to estimate rates or premium
Premium = future( losses + loss adj expenses + fixed expenses + variable expenses + profit + contingencies)
Pure Premium method
R-ind = (P + F) / (1 - V) = Prem/E = indicated rate per exposure
P = L/E = loss per exposure or Pure Premium L = dollars of loss and LAE F-exp = dollars of fixed expense V-exp = dollars of variable expense V = dollars of variable expense/Prem = Vexp/Prem F = F-exp/E = fixed expense per exposure
Loss Ratio Method
R-ind/R0 = ELR/TLR
R-ind = indicated rate per exposure
R0 = current rate per exposure= Prem0/E
Experience Loss Ratio = ELR = L/Prem0
Target Loss Ratio = TLR = (1 - V)/ (1 + Fexp/L ) = (1 - V) / (1 + F/P)
***Note that the Loss Ratio Method Produces an Indicate Rate Change - Multiply by R0 to determine the indicated rate
Pure Premium Method vs. Loss Ratio Method
Based on - PP: Exposure; LR: Premium
Requires existing rates - PP: No; LR: Yes
Requires on-level premium - PP: No; LR: Yes
Produces - PP: indicated rates; LR: indicated rate changes
Law of large numbers
As the number of trials of a random process increases, the percentage difference between the expected and actual values goes to zero. ‘The more data we have, the more we believe what the data says’
Properties of Credibility
0<= Z <= 1 (if Z = 0, data receives no credibility, if Z = 1, data is fully credible) Change in Z / Change in E >=0 (credibility increases as the volume of experience data increases) Change in (Z/E) / change in E <=0 (credibility increases at a non-increasing rate as the volume of experience data increases)
Z = credibility value E = measure of data volume
Two methods of assigning credibility
- Classical (limited Fluctuation or Square Root Rule)
- Buhlmann (least squares or Greatest Linear Accuracy
- Others, including judgmental methods
Classical Credibility
Z = sqrroot(n/k)where n = volume of experience data and k = full credibility standard
**Note that if n>=k, then Z = 1
Buhlmann Credibility
Z = n/ (n+k)
n = volume of experience data
k = quantified amount of variation; the higher the variation with respect to the experience data the lower the credibility of that data
**Note that k has a different meaning than for classical Credibility, hehre k represents 50% credibility standard
**Notice that Z can never reach 100% (or full credibility) under this approach)
Truncation and Credibility
When credibility is calculated, the resulting values are not rounded. We wish to avoid giving the data more credibility than is warranted, thus the values are always truncated to the desired precision
Credibility Table
- Often constructed to provide a simple lookup capability to determine what credibility value to assign to a volume of data
- Loss of accuracy, but the tables provide more transparency
Compliment of credibility (if certain volume of data has 70% credibility, what do we assign the other 30% to?)
- No change (when calculating a rate change)
- Expected Result (when calculating a rate)
- Multi-State Data (if using Single-State Data)
- Statewide Data (if using single-Territory Data)
- Multi-Class Data (if using Single-Class Data)
Formula to connect Credibility and Complements
Z x Data + ( 1 - Z ) x Complement
** in ratemaking use: Z x Observed Loss Ratio + ( 1 - Z ) x Expected Loss Ratio
Use of Weighted Credibility
Several years of data are used to obtain a prediction (Use credibility weighting to assign more credibility to more recent data)
Z x credibility weighted loss ratio + (1 - Z) Expected loss ratio
Excess Procedure
- Many insurance lines use multiple years of data for calculating prospective loss costs
- Usually, the lines that are more volatile rely on a longer experience period
- Balance stability with responsiveness
- Some perils may be more volatile than others, and require the use of an ‘Excess’ procedure based on historical data (beyond the experience period)
How does an excess procedure work?
- Classifies losses as either ‘normal’ or ‘excess’ based on some threshold
- Excess losses are removed from the experience period and replaced with a long term average
Limitations of traditional ratemaking methods based on historical loss and premium data
- Not enough historical insurance data
- changes in land use, population densities, construction techniques and methods, building codes, safety regulations, etc.
- Changes in premium adequacy over time
- Not all portions of a state are equally exposed
- *sometimes we have to resort to judgment or computer models
