ACTSC 625 P&C and Health Insurance Mathematics

ACTSC 625P&C and Health Insurance Mathematics Lecture 1 Introduction to short term insurance 8/1/13 ACTSC 625 L1: Intro P&C

Introduction • See website for outline etc learn.uwaterloo.ca • Textbook: • Loss models (4thEdition), by Klugman Panjer and Willmot, Wiley • Supplementary materials introduced as required. • Board notes and slides are important ACTSC 625 L1: Intro P&C

Course Objectives • Describe standard features of non-life insurance and re-insurance policy design. • Understand / work with standard frequency and severity models for insurance losses. • Determine the impact of deductibles and reinsurance on the models and estimation. • Understand and calculate moments and probabilities for compound distributions, especially compound Poisson, compound binomial, and compound negative binomial. • Apply Bayesian estimation to loss models. • Understand and calculate Buhlmann-Straub and exact Credibility premiums. • Understand principles of claims reserving for non-life insurance, using run-off triangle methods. • Understand introductory ruin theory. ACTSC 625 L1: Intro P&C

Notes • The outline gives the planned schedule – subject to change. • This is a very ambitious syllabus! ---- Dr. Hardy • This course relies heavily on Actsc 613 – heavy on stats and probability. Also picks up from Actsc 623 and Actsc 624. • We will be using Excel to some extent. • This course covers around 65% of SOA Exam C/CAS Exam 4. ACTSC 625 L1: Intro P&C

P&C Insurance Name some different types of P&C insurance: • Auto • Home • Catastrophe (earthquake, flood, hurricane, etc) • Disability • Crime • Worker’s compensation Which of these would be most suitable for statistical analysis? Why? How would we analyze the others? ACTSC 625 L1: Intro P&C

P&C compared with Life The major differences: • Term of contract • Uncertainty in claim severity; uncertainty in claim frequency • Underwriting • Adverse selection • Policy modifications • Fraud • Impact of investments and economic cycles ACTSC 625 L1: Intro P&C

Some P&C Fundamentals • Insurable Risks – what are they? What would not be insurable? • Risk Aversion – why do we buy insurance? How much are we prepared to pay? • Rating factors –information required to determine premium for a risk. • Exposure measures -- how do we measure risk and express premiums? • Adverse Selection – impact of underwriting and rating factors • Moral Hazard – how does it impact insurer? Mitigation? ACTSC 625 L1: Intro P&C

Insurable Risks • The loss should be random and unpredictable (and not controllable by insured) • The loss should be quantifiable, verifiable, and significant to the insured • Risks should be diversifiable • There should be an economic premium which covers the cost of the risk to the insurer and which a risk averse individual insured is willing to pay. • The loss should be relatively rare* • The loss should be limited. ACTSC 625 L1: Intro P&C

Risk Aversion • Suppose Kim is concerned about theft of her bicycle. • Replacing her bike would cost X ~ Unifrom[100,300] • There is a 3% probability that her bike will be stolen. • What is the expected value of her loss? • Is this risk insurable? • Suppose she has exponential utility, with parameter 0.005; would she buy insurance for $10? ACTSC 625 L1: Intro P&C

Rating factors • What information would you seek to insure Kim’s bicycle? • What about auto insurance? • Homeowners? Rating factors should separate policies into homogeneous groups for determining the premium. ACTSC 625 L1: Intro P&C

Rating factors - criteria • Statistically significant wrt cost and in differentiating risks • generate risk classes which are ‘credible’ • objective • verifiable • consistent with industry standards • economical • legally and socially supportable • encourage risk-reducing behaviour ACTSC 625 L1: Intro P&C

Exposure Measures • The exposure measure is used to measure the risk for a policy, and is the basis for the premium calculation. • Base premium rates are generally expressed per unit of exposure. • Exposure measures should be • Proportional to the expected loss • Consistent with industry standard measures • Practical (quantifiable, objective, economical) • Often use the rating factor which best meets these criteria ACTSC 625 L1: Intro P&C

Exposure Measures • Suggest exposure measures for: • Homeowners insurance • Worker’s Compensation (also known as Employer’s Liability) • Commercial Fire Insurance • Professional Liability ACTSC 625 L1: Intro P&C

Adverse Selection • Define adverse selection. An individual's demand for insurance is positively correlated with the individual's risk of loss (like higher risks buy more insurance), and the insurer is unable to allow for this correlation in the price of insurance • Why do insurers want to minimize adverse selection? The reason is quite obvious. • How do insurers control adverse selection? Specify exposure measure. More information. More factors. This may reduce size of data and the power of statistical inference. ACTSC 625 L1: Intro P&C

Moral hazard • Define moral hazard protecting their clients from risks (like fire, or car accidents) might encourage those clients to behave in riskier ways (like smoking in bed or not wearing seat belts). • Why do insurers want to minimize moral hazard risk? The reason is quite obvious. • How do insurers control moral hazard? Specify policy. Use deductibles. Unify the interest of the insurer and the insured. ACTSC 625 L1: Intro P&C

Policy Modifications • Deductibles • Ordinary • Franchise • Disappearing • Policy Limits • Co-insurance ACTSC 625 L1: Intro P&C

Policy Modifications • Why do insurers use them? • How do policyholders use them? • How do they impact reporting and recording of losses? • Reinsurers also use policy modifications. ACTSC 625 L1: Intro P&C

ACTSC 625 P&C and Health Insurance Mathematics