Roger Loomis, FSA, MAAA Jim Berger, FSA, MAAA June 25, 2012 Kansas City Actuaries Club

1. The New World of Long-Term Care and Disability Income Modeling The New World of Stochastic Modeling Roger Loomis, FSA, MAAA Jim Berger, FSA, MAAA June 25, 2012 Kansas City Actuaries Club

2. “Models should be made as simple as possible, but not simpler.” -Albert Einstein

3. For DI and LTC, Monte Carlo simulation models dominate deterministic models: • Simulation models are more insightful • Simulation models are simpler

4. Management Forecasting Example Big Easy Insurance Company (motto: Let the Good Times Roll!) Mid-sized carrier Publically owned Multiple lines Moderate sized LTC Block (10,000 lives) Most policies have a shared-care benefit Needs a management forecast

5. What Model Should We Use? Broad Categories • Claim Cost • Deterministic First Principles • Monte Carlo Simulation

6. Forecasting with Claim Costs • Key features of claim cost approach • A single number represents entire expected cost of claims for each future incurral period • Typically stored in large tables with multiple adjustment factors • Used in calculation of policy reserves • Claim Costs for Shared Care calculated using simulation techniques

7. Advantages of Forecasting with Claim Costs Claim costs readily available from valuation system Can fit into a life insurance projection system Fast and easy to run Easy to audit projection Theoretically compatible with source of earnings analysis

8. Disadvantages of Forecasting with Claim Costs Sometimes difficult to calculate claim costs Forecast is blunt—results in incurred claims rather than paid claims and claim reserves Difficult to reconcile with operational metrics In practice, source of earnings analysis is difficult to implement

9. Forecast of 1Q 2013

10. Fast-Forward 9 Months Management was expecting profits for 1Q2013 in the neighborhood of $300,000 Actual results show a profit of only $38,000 Huge disappointment Discrepancy driven by reserves You have 6 hours to prepare an explanation for management

11. 1Q 2013 Actual and Expected

12. Insights from CC Model Incurred claims much higher than expected Policy reserve increase higher than expected Low lapses explain change in policy reserve

13. Unanswered Questions from CC Model • What is driving the high incurred claims? • New incurrals too high? • Recoveries too low? • Can low lapses be attributed to random fluctuations? • Can high incurrals be attributed to random fluctuations? • Is there evidence that the underlying assumptions are wrong? • Is management action needed?

14. First Principles Model Better?

15. Deterministic First Principles Model

16. 2nd Month

17. 3rd Month

18. Deterministic First-Principle Models • Result in grid of size ω2 ÷ 2 • For example 240 months  28,800 cells • Relatively Unwieldy • Relatively Slow Runtimes • But Relatively Manageable

19. Deterministic First-Principle Models • Key Limitations • Recoveries reenter active pool • No memory of having been on claim • Implicitly assumes restoration of benefits • Can’t handle shared care

20. Let’s make Slight Enhancement • Add memory of having been on claim • Motivated by • Refined incidence rates for relapses • No restoration of benefits • Return-of-premium (less claims) • Pools of money for multiple benefits • Shared care • Combo products

21. With Enhancement

22. 2nd Month

23. 3rd Month

24. Path-Dependent Deterministic Models • Result in 2ω paths • E.g. 240 months  2240 Paths

25. This Slight Enhancement is Impossible • Deterministic models can’t handle path-dependent benefits on a first principles basis • Deterministic models are inherently limited • We are forced to do some hand waving to incorporate shared care

26. Deterministic First Principles

27. Additional Insights With the Model • Change in incurred claims primarily driven by claim reserves • Recovery rate is lower than expected • Incurral rate is higher than expected

28. Drawbacks of First-Principles Deterministic • Still unanswered questions: does discrepancy indicate an underlying problem, or is it within the bonds of expected variation? • Rigid structure—can’t directly model certain benefits • Difficult to audit • Slow runtimes

29. Forecasting with Monte Carlo Simulation • Key features of Monte Carlo approach: • Basic assumptions are probabilities of going on claim, recovering, lapsing, dying, and otherwise changing states • Directly models state changes that determine premiums and benefits • Estimates full probability distributions of financial line items and operating metrics

30. Understanding Simulation Models Overriding assumption: We precisely know the probability of lapsing, dying, going on claim, and recovering Variation only due to risk like the risk a casino faces: random variation driven by known probabilities Remember that in reality, business is riskier than simulation models imply Sensitivity testing still needed

31. Simulation of 1Q2013 Lapses

32. 1Q 2013 New Claims

33. Reserves Released Because of Recoveries

34. Simulations of 1Q 2013 Profits

35. Profit Emerge in a Rough Pattern

36. Over Lifetime of Block, the Roughness Tends to Cancel Itself Out

37. Sample Monte Carlo Forecast Results

38. Insights from Simulation Management should have expected results in the range of $0 to $500,000, and not necessarily close to $300,000 mean New claims and recoveries both within 90% confidence interval (barely) No strong statistical evidence that lapse rates, incurral rates, and recovery rates are wrong No strong statistical evidence that business is being mismanaged Claims and recoveries should be carefully monitored to see if this trend continues

39. Advantages of Monte Carlo Approach Calculations are muchsimpler than deterministic approaches Easier to explain to management how the model works Easily handles path-dependent benefits and path-dependent probabilities (e.g. probability of claims relapsing) Provides simulated results that replicate operational metrics (number of claims, recoveries, etc.) Cont.

40. More Advantages of Monte Carlo Approach • Null hypothesis is that incidence, termination, and lapse/death probabilities are correct • Model provides confidence intervals on every metric—if results are within that range, experience is consistent with null hypothesis that we correctly understand the risk • Results falling outside of range indicates there is an issue that needs to be investigated: • Underwriting problems • Claim adjudication/management issues • Bad assumptions • Changing landscape

41. More Thoughts on Stochastic Models When describing results, use weatherman language (e.g. “Our computer models indicate that we might have between 35 and 58 new claims next quarter”) Don’t be confident results will be within confidence interval Results falling out the intervals is merely evidence of that the model’s parameters are wrong or the business isn’t being managed properly

42. Final Thoughts on Stochastic Models For DI and LTC, Monte Carlo simulation models dominate deterministic models: • Simulation models are more insightful • Simulation models are simpler

44. Why Do We Use Models? The goal of modeling is to better manage business • For insurance: better manage risk • Avoid certain risks; • Acquire, retain, and exploit other risks; • Reduce or transfer unnecessary risks • Thus, management needs to understand the risk to the best degree possible. But…

45. Why Do We Use Models? The goal of modeling is to better manage business How are decisions really made? Balance complexity with ducky-horsy Parsimony - economy in the use of means to an end Consider time, resources, the ultimate requirement (e.g., precision), mngt skills Some problems are inherently stochastic

46. What Is A Stochastic Model?The goal of modeling is to better manage business • Varies interest rates • Varies benefits • Mortality • Morbidity • Lapse

47. Types of Stochastic ModelsThe goal of modeling is to better manage business • Variables may be • Path-dependent • Interest rates • Path-dependent options • Return of premium less claims paid • Last-to-die “heartbreak syndrome” – life and annuities • Spouse/child riders on life policies

48. Types of Stochastic ModelsThe goal of modeling is to better manage business • Variables may be • Path-independent • Mortality • Binomial • Major medical claims • More complex distribution

49. Types of Stochastic ModelsThe goal of modeling is to better manage business • Some models considers impact of specific variable(s) • Asset adequacy testing • Randomly generated outside model and run deterministically • Monte Carlo simulation – might vary many variables • Randomly generated inside the model • What is the purpose? Do we really need to vary all variables? How do we communicate partial knowledge?

50. Types of Stochastic ModelsThe goal of modeling is to better manage business • Monte Carlo simulation of DLR • 250 claims, utilization rates at 100% • $21,776,000, $1.212mm is 95%CI or ~5.5% • 250 claims, utilization rates vary by duration and claim characteristics • Utilization is deterministic; path dependency is hard to model • $21,460,000, $1.415mm is 95%CI or ~5.9% • Greater variance likely due to more things that can vary – utilization • Share Care rider – presented previously • If we don’t know parameters, what will model tell us? • If we have experience data, can this avoid stochastic models?