Intensive Actuarial Training for Bulgaria January 2007

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

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

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

Effect of Risk Averaging for Insurance Company • For, in dependent random variables, Xi ‘s, Var (X1 + X2 + X3 +…+ Xn) =  Var(Xi) • If the Xi ‘s are from the same risk class, I.e. they have the same mean and variance, then • Var(Xi) = n Var(X) • Var((Xi)/n) = n Var(X)/n2 = 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

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

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

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

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

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

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

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

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

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

Credibility Factor Z • Reflective of the extent of experience • Some properties of Z: • 0  Z  1 • dZ/dE > 0, where E is exposure • d2Z/dE2 < 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

Intensive Actuarial Training for Bulgaria January 2007