Principles Underlying Actuarial Science Session C 17 Presentation at the CAS Fall Meeting

1. Principles Underlying Actuarial Science Session C 17 Presentation at the CAS Fall Meeting San Francisco Prepared by Mark Allaben

2. Joint CAS/SOA Committee on Actuarial Principles San Francisco CAS Meeting Presentation November 12-15, 2006 Prepared by Mark Allaben

3. Acknowledgements Presentation is adopted from work by Stuart Klugman and Arnold Dicke presented at the SOA Annual Meeting October 18, 2006 Prepared by Mark Allaben

4. Committee Members • Mark Allaben, Stuart Klugman, Co-Chairs Current Membership • Arnold Dicke, Chris Diamantoukas • Sam Gutterman, Richard Lord • Warren Luckner, Bob Miccolis • Joe Tan Prepared by Mark Allaben

5. Agenda • History • Status of Committee Work • Committee Request of the CAS Board • Next Steps • Overview of Principles Prepared by Mark Allaben

6. History – Joint Work With SOA • 1991 – SOA Board accepted a statement of principles. • Approved as a statement by the committee. • No member vote. • Not an opinion of the SOA. • Published in TSA XLIV in 1992 – Discussion draft distributed, comments received. Prepared by Mark Allaben

7. History – Joint Work With SOA • 1997 – Discussion draft distributed, comments received. • 1999 – Exposure draft distributed, extensive comments received. • Committee has worked since then on the next draft. Prepared by Mark Allaben

8. Current Status • New exposure draft sent to CAS Executive Council for review • CAS Executive Council approved new exposure draft to be sent to CAS Board for review • New exposure draft presented to SOA Board • Outcomes of SOA Board Meeting • Instructed Committee to finalize current draft, to send final draft to legal counsel and e-mail legally reviewed draft to Board via e-mail for approval to expose to Society Prepared by Mark Allaben

9. Committee Request • CAS Board Actions: • Authorize committee to finalize document • Authorize committee to send final document for legal review • Instruct committee to send CAS Executive Council and CAS Board final legally reviewed document Prepared by Mark Allaben

10. Process Next Steps • Gain CAS Board Approval. • Receive comments on exposure draft from CAS and SOA members. • Principles Committee revise accordingly. • Bring to CAS/SOA Boards for endorsement. • A two-thirds majority of the Boards is required for approval. Prepared by Mark Allaben

11. Overview of Principles • What are principles and why are they needed? • Overview of the four sections. • Statistical framework. • Economic and Behavioral Framework. • Risk Management and Actuarial Modeling. • Financial Security Systems Prepared by Mark Allaben

12. What are Principles? • They are the key elements of the scientific framework that underlies actuarial practice. • They are grounded in observation and experience. • They do not specify how actuarial work is to be done (that is the purpose of standards). Prepared by Mark Allaben

13. Why Articulate Principles? • Describe and strengthen the intellectual foundation of our profession. • Provide a foundation for the extension of actuarial models to new applications. • Guide the articulation of practice-specific principles. Prepared by Mark Allaben

14. Why Articulate Principles? • Further actuarial education. • Focus research efforts. • Aid in strategic planning. • Provide an indication of what actuaries can and cannot do. Prepared by Mark Allaben

15. Statistical Framework • Begin with standard definitions of experiments, stochastic phenomena, probability, random variables, and estimators. • Recognize uncertainty, which can be quantified (and variance need not be the only measure). Prepared by Mark Allaben

16. 1.1 Statistical Regularity • The law of large numbers. • Enough observations will enable one to understand the probabilities and other measures. • Does not reject subjective approach to probability. Prepared by Mark Allaben

17. 1.2 Model Construction • It is possible to model stochastic phenomena. • Models can be deterministic or stochastic. • Because models only represent reality, it is possible to have a model of a random phenomenon that is not random. Prepared by Mark Allaben

18. Sources for Model Building • Outcomes of experiments (e.g., mortality study) • Observations of related phenomena (e.g., use census data) • Knowledge of the phenomenon itself. • Can use all three. Prepared by Mark Allaben

19. 1.3 Credibility • A weighted average of several estimators may be more accurate than any of the component estimators. • Need a way to measure accuracy of a model. Prepared by Mark Allaben

20. Economic and Behavioral Framework • Need to explain behavior in terms of quantifiable incentives and disincentives. • These principles are less specific because they describe human behavior and thus preferences Prepared by Mark Allaben

21. 2.1 People Like Some Things Better than Others (Preferences) • When confronted with a choice of two goods people can identify that they either like one more than the other or truly do not care. • So people will trade when it is to their perceived advantage. Prepared by Mark Allaben

22. 2.2 People Do Not Have the Same Preferences (Diversity of Preferences) • Sometimes one person prefers A to B while another person prefers B to A. • By setting up the possibility of exchanges, it is necessary to define assets, liabilities, options, and swaps. Prepared by Mark Allaben

23. 2.3 Time Value of Money(Time Preference) • Most people prefer to receive something sooner than to receive the same thing later Prepared by Mark Allaben

24. 2.4 Risk Averse • Faced with two uncertain futures with equal expected values but different measures of uncertainty, people tend to choose the future with lower uncertainty. • Risk-seekers exist, but rarely in settings of actuarial interest. Prepared by Mark Allaben

25. 2.5 Money Exists • Eventually everything needs to be expressed in monetary terms. This principle reflects the observations that most all economies use money. • As a result, people put monetary value on economic goods. Prepared by Mark Allaben

26. Present Value • This is not a principle, but it is necessary to observe that present value functions on cash flows can be constructed. • A challenge is in defining present value when the future is random. • We use scenarios, their probabilities, and the resulting present value random variable. • This allows us to define concepts such as value at risk and conditional tail expectation. Prepared by Mark Allaben

27. 2.6 Enlightened Self-Interest • While people act according to their preferences, they also use the knowledge they have about other parties and about the environment. • This recognizes the possibility if information asymmetry. Prepared by Mark Allaben

28. 2.7 Market Value Models • These models allow us to estimate what an item will trade for. Done by estimating the actions buyers and sellers are likely to take. • Equilibrium and no arbitrage models are examples. Prepared by Mark Allaben

29. 2.8 Law of One Price • Two portfolios that have the same cash flow will trade at the same price. • Leads to the use of replicating portfolios and no arbitrage pricing. Prepared by Mark Allaben

30. Risk Management and Actuarial Modeling • Here we identify what is unique about an actuarial phenomenon (they involve the actuarial risk variables of frequency, timing, and severity). • It must occur in the context of an economic system and have more than one possible outcome. Prepared by Mark Allaben

31. Example – Fire Insurance • Phenomenon is all fires that strike an insured building. • Number of fires and the time of occurrence is random. • Each fire results in random payments – to the insured for damages, and for processing and adjudicating the claim. Prepared by Mark Allaben

32. 3.1 Scaling • Exposure measures exist. • Examples include the face amount of insurance, the number of cars insured, the number covered in a medical plan. Prepared by Mark Allaben

33. Risk Management • Components are identification, assessment, and then management, perhaps via risk transfer. • A risk management system fails when a pre-defined condition (such as statutory insolvency) occurs. Prepared by Mark Allaben

34. 3.2 Combining Risks • Risk management often involves combining risks. This principle notes that risk associated with a combination is affected by the correlations. • Leads to a discussion of pooling, diversification, and hedging. Prepared by Mark Allaben

35. 3.3 Actuarial Present Value • It is possible to construct models that will assign present values that will be close to what a person would assign to that same set of financial transactions. • In plain words, we can deduce a value for an insurance contract that lead to pricing it where people will buy. Prepared by Mark Allaben

36. 3.4 Continued Model Validity • Over time the quality of a model may deteriorate. Factors include • Environmental changes. • Changes in understanding of the environment. • Data becoming outdated. Prepared by Mark Allaben

37. 3.5 Failure Probability • The confidence in an estimated failure probability depends on • The risks being managed. • The system used to manage them. • The model constructed to yield the probability. • Risks not accounted for. Prepared by Mark Allaben

38. Financial Security Systems • This is a risk management system in which participants transfer actuarial risks and their consequences to a second party in return for making a payment. • Includes life insurance, life annuities, retirement plans, health-care financing systems. • Can be voluntary or mandatory. • The participants may be capable of being measured in a way that leads to risk characteristics (such as gender, age, weight). Prepared by Mark Allaben

39. 4.1 Risk Classification • Risk characteristics can be identified such that • Each participant can be assigned to a risk class. • If two participants have the same characteristics, they are assigned to the same class. Prepared by Mark Allaben

40. 4.2 Refining Risk Classes(Effect of Refinement) • Risk classes can be divided. For example, could start with 10 year age groups then switch to 5 year age groups. • Refinement leads to opposing forces on accuracy. • Increased homogeneity increases accuracy. • Reduction in data decreases accuracy. Prepared by Mark Allaben

41. Consequence of Risk Classification • Can construct a rate structure that assigns premiums to each risk class. Prepared by Mark Allaben

42. 4.3 Antiselection • Lack of an appropriate refinement will alter the rates of participation. • Example – offering the same premium to smokers and non-smokers will lead to more participation by smokers. Prepared by Mark Allaben

43. 4.4 Moral Hazard • The existence of a contract creates the potential for decisions by one party subsequent to the transaction which might have an adverse impact on the other participant. Prepared by Mark Allaben

44. 4.5 Actuarial Soundness • This is the bottom line, it is the probability that the financial security system will meet its success criterion. • It depends on the risks covered, the premiums changed, and the assets held to provide for the risks. Prepared by Mark Allaben

45. Casualty Actuarial Society 4350 N. Fairfax Drive, Suite 250 Arlington, Virginia 22203 www.casact.org Prepared by Mark Allaben