1 Ken Fikes, FCAS, MAAA Introduction to Casualty Actuarial Science November 2005

2 Ken Fikes, FCAS, MAAA Casualty Actuarial Science Two major areas are measuring 1. Written Premium Risk l Pricing 2. Earned Premium Risk l Reserving

3 Ken Fikes, FCAS, MAAA Pure Premium Ratemaking Pure Premium = P = C/E * L/C = L/E Claims (C) 1,000 Car Years (E) 10,000 Losses (L)$1,100,000 P = (1,000 / 10,000) * ($1.1M / 1,000) = $110

4 Ken Fikes, FCAS, MAAA Pure Premium Ratemaking Fixed expense per exposure (F) $10 Variable expense factor (V)17.5% Profit and Contingencies factor (Q) 2.5% R = ($110 + $10) / (1 – – 0.025) = $150

5 Ken Fikes, FCAS, MAAA Trends in the Pure Premium l Severity »Inflation, Jury Awards, Medical Expenses l Frequency »Court Decisions, Legal/Social Pressures l Exposure »Payroll, Auto Values

6 Ken Fikes, FCAS, MAAA l What is a Loss Reserve? Amount necessary to settle unpaid claims l Why are Loss Reserves Important? Accurate evaluation of financial condition & underwriting income Definitions

7 Ken Fikes, FCAS, MAAA Definitions l Accounting Aspects of Loss Reserves Assets Liabilities Surplus Balance Sheet

8 Ken Fikes, FCAS, MAAA Definitions l Case Reserves »Claim reported but not yet paid »Assigned a value by a claims adjuster or by formula l Bulk + IBNR reserves include: »Reserves for claims not yet reported (pure IBNR) »Claims in transit »Development on known claims »Reserves for reopened claims

9 Ken Fikes, FCAS, MAAA Life Cycle of a Claim Reserve 8/1/01 Accident entered into records as $1,000 Formula Reserve 7/11/01 Accident reported Claims in Transit 10/5/01 Individual reserve established $10,000 Case Reserve 1/1/02 Estimate revised $25,000 Case Reserve 8/18/02 Settlement agreed $30,000 Case Reserve 8/25/02 Payment sent $30,000 Case Reserve 9/2/02 Claim draft clears Closed 4/2/01 Accident occurs Pure IBNR

10 Ken Fikes, FCAS, MAAA Other Considerations l Factors Affecting Loss Reserves »Internal or Operational –Reinsurance programs –Claims handling practices –Business growth –Case reserve adequacy –Mix of business –Underwriting –Contract changes –Structured settlements –Portfolio characteristics

11 Ken Fikes, FCAS, MAAA Other Considerations l Factors Affecting Loss Reserves »External or Environmental –Society –Regulation –Judiciary –Seasonality –Residual Market –Inflation –Economy

12 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Definitions l Loss Development The financial activity on claims from the time they occur to the time they are eventually settled and paid. l Triangles Compiled to measure the changes in cumulative claim activity over time in order to estimate patterns of future activity. l Loss Development Factor The ratio of losses at successive evaluations for a defined group of claims (e.g. accident year).

13 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Compilation of Paid Loss Triangle l The losses are sorted by the year in which the accident occurred. l The losses are summed at the end of each year. l Losses paid to date are shown on the most recent diagonal. l The data is organized in this way to highlight historical patterns.

14 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Compilation of Paid Loss Triangle l The goal is to estimate the total amount that will ultimately be paid

15 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Paid Loss Development Factors From the end of the accident year (at 12 months) to the end of the following year (at 24 months), paid losses for 1997 grew 79%. During the next year (from 24 to 36 months), paid losses experienced an additional 24% growth (or development) and so forth. Loss Development Factors (LDFs) are also known as: Age-to-Age factors Link Ratios

16 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Paid Loss Development Factors

17 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Application of Paid LDM

18 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Paid LDM Projections & Reserves l Loss Reserve 12/31/01 = $ million

19 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Compilation of Incurred Loss Triangle

20 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Selected Incurred LDFs

21 Ken Fikes, FCAS, MAAA Basic Reserving Techniques: Incurred LDM Projections & Reserves l Loss Reserve 12/31/01 = $ million

22 Ken Fikes, FCAS, MAAA Key Assumptions & Potential Problems Assumptions Sample Problems Claims settlement patterns unchanging Case reserving practices & philosophies unchanging No claim processing changes Policy limits have no impact on loss development Increasing delays in claim closing rates Conscious effort to improve case reserve adequacy; Introduction of new case reserving procedures Change in data processing; Revised claim payment recording procedures Increasing frequency of full policy limits claims; Changing policy limits

23 Ken Fikes, FCAS, MAAA Key Assumptions & Potential Problems Assumptions Sample Problems Loss development unaffected by changing loss cost trends No change in mix of business No cyclical loss development No data anomalies Surges in inflation; Increased litigation; Diminished policy defenses Changes in reinsurance coverages; Increased long-tail exposures; Introduction of new or revised coverages Claims settlement or reserving impacted by business underwriting cycles Catastrophic or unusual losses reflected in loss experience; Unusual claim settlement/reporting delays

24 Ken Fikes, FCAS, MAAA Comparison of Estimated Reserves

25 Ken Fikes, FCAS, MAAA Example

26 Ken Fikes, FCAS, MAAA Solution

27 Ken Fikes, FCAS, MAAA Further Reading For additional information on Loss Reserving, see the following references at Wiser, et al., “Loss Reserving,” Foundations of Casualty Actuarial Science (Fourth Edition), Casualty Actuarial Society, 2001, Chapter 5, pp Bornhuetter, R.L; and Ferguson, R.E., “The Actuary and IBNR,” PCAS LIX, 1972, pp Including discussions of paper: Cooper, W.P., PCAS LX, 1973, pp ; and White, H.G., PCAS LX 1973, pp Brosius, E., “Loss Development Using Credibility,” CAS Study Note, March 1993.