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CIA General Meeting

CIA General Meeting. October 19-20, 2006 Chicago, Illinois. Session IP-31. Stochastic Models: Application to LTD. When is a stochastic model appropriate? Why stochastic LTD? How?. Stochastic LTD Models. Ideas presented are very Blue Sky My goal to provoke thought Not that hard to do

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CIA General Meeting

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  1. CIA General Meeting October 19-20, 2006 Chicago, Illinois Session IP-31

  2. Stochastic Models: Application to LTD • When is a stochastic model appropriate? • Why stochastic LTD? • How?

  3. Stochastic LTD Models • Ideas presented are very Blue Sky • My goal to provoke thought • Not that hard to do • Excel model

  4. When Are Stochastic Models Appropriate? • When the loss model has • a long or heavy right tail • A “cliff” or trigger point • Dependencies of Risk

  5. Looking At LTD Models • Traditionally viewed as a life annuity • We can also view these as a random variable with probability distribution

  6. Why Not Look at LTD This Way?

  7. Why Not Look at LTD This Way? Heavy tail Trigger Point

  8. Why Use the Same Formula for These Loss Models?

  9. Dependencies of Risks Between Claims • LTD Experience is influenced by • Economic conditions • Geographic location • CPP policy • Court decisions • Legislation • All of these lead to a dependency between claims

  10. Dependencies of Risks Between Years • Relationship between incidence and termination rates • High incidence rates may mean more softer claims • Higher termination rates in subsequent years • Low incidence rate may mean “harder” claims • Cyclical termination rates • Claims clean up focuses on soft claims • Followed by period of low termination rates • High turnover in adjudicators leads to low terminations • Followed by period of high termination rates • This year’s experience influences next year’s experience

  11. Simple Stochastic Model • 1000 Trials • Each trial represents one possible outcome for the portfolio • For each trial • Simulate the time on claim for each life • Use CIA LTD table to determine distribution of time on claim • Sum the PVs for all lives

  12. Test Case 1 • 500 lives from a real LTD block • Mature block of claims • High female content

  13. Test Case 1 Results • Mature block of 500 claims • Results fairly stable • Limited up side risk

  14. Test Case 1 Results

  15. Test Case 2 • Subset of Test Case 1 • 100 lives within 2 years of disability • Representative of new LTD group

  16. Test Case 2 Results • Note a 5% Pad indicates 95% of monthly termination rates • Results less stable (Smaller group, within Own Occ period, younger lives)

  17. Test Case 2 Results

  18. Does the law of large numbers apply? • Test Case 1 indicates that risk is greatly reduced in a large, mature block • Good experience offsets bad • But … • Cyclical nature of LTD means that all groups have bad years together • If we write refund LTD, we give the good experience back and keep the bad

  19. Uses For Stochastic LTD Models • Supplement not replace deterministic models • Better understanding of risks • Stop loss and Durational Pooling charges • Refund LTD reserves

  20. Accounting for Dependencies of Risks • Add a random variable • allow for good or poor years • affects all lives equally • key impact in early years • Modification to termination probability for each year • Autoregressive component for cycles?

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