1. Intensive Actuarial Training for Bulgaria January 2007 Lecture 5 – General Insurance Overview and Pricing By Michael Sze, PhD, FSA, CFA

2. Insurable Risk To be insurable, the risk must be –Definite –Accidental in nature Insurance: to avoid risk, not to get profit Speculation: speculator takes the risk in hope of making profit from it Gambling: create unnecessary risk

3. Risk, Peril, and Hazard Risk – possible variation in economic outcome Peril – cause of risk (fire, collision, theft) Hazard – a contributing factor to peril

4. Effect of Risk Averaging for Insurance Company For, in dependent random variables, X i ‘s, Var (X 1 + X 2 + X 3 +…+ X n ) =  Var(X i ) If the X i ‘s are from the same risk class, I.e. they have the same mean and variance, then Var(  X i ) = n Var(X) Var((  X i )/n) = n Var(X)/n 2 = Var(X)/n In other words, variance of the average of n risks is equal to (1/n) of the variance of each  for the insurance company =  for policy holder/  n

5. Major Types of Property Casualty Insurance Automobile insurance Homeowners Insurance Workers Compensation Fire/Marine Insurance Liability Insurance

6. Automobile Insurance Liability: if you injure people or damage property Medical: personal injury Uninsured motorist: in case the other party of the accident, even though at fault, does not have adequate insurance to pay damages Collision

7. Home Owner Insurance Covers damage to house by names perils There is deductible May have coinsurance too If C is coverage, coinsurance % is %C, damage is D, market value of property is MV, then payment P is given by: P = D x C/(%C x MV), up to a limit, < D

8. Example for Home Owner Insurance MV of assets = 1,000,000 % Possible Coverage C = 80% Coverage purchased = 500,000 So, proportional coverage = 5/8 If damage D = 2,000 Then, payment = 2,000 x 5/8

9. Home Owners Insurance Covers Basic coverage: house Additional coverage: garage, out-building, property in house, living expenses during repairs Liability insurance: if sued due to property

10. Workers’ Compensation Coverage: job related injury of workers Benefits: unlimited medical care Disability insurance Death benefit Rehabilitation

11. Rate Making - Pricing Claim frequency f: from recent experience Average f = # of incurred claims / units of earned exposure Severity S = average payment per claim = $ of incurred loss / # of incurred claims Claim Cost = f x S = net premium

12. Adjustments to Claim Cost Claim reserve: to cover later claim, incurred but not reported Inflation trend: inflation, legal, technical advances, economics

13. Other Components of Price Expenses: loss adjustment expenses, commissions,premium taxes, administration Expense rate = All expenses as % of GP Permissible loss ratio PLR= 1–expense ratio Gross Rate = Incurred Loss per Unit /PLR If expense is partly fixed F and partly variable V, I.e. dependent on GP, then Gross Rate = (Incurred Loss per Unit +F)/(1-V) Loading for profit and contingency

14. Credibility Factor Z Reflective of the extent of experience Some properties of Z: –0  Z  1 –dZ/dE > 0, where E is exposure –d 2 Z/dE 2 < 0 Two method to estimate Z; –Z = E/(E+K), where K is variability –Z =  (n/N), where n is # of claims and N is the number of claims to get full credibility