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A DYNAMIC APPROACH TO MODELING FREE TAIL COVERAGE

A DYNAMIC APPROACH TO MODELING FREE TAIL COVERAGE. Robert J. Walling, ACAS, MAAA 2000 CLRS. The Goal. Starting With The Walker Model, Add Modifications Necessary to Reflect: 1) Current Policy Characteristics 2) Current Life Actuarial Work 3) Elements of DFA Including:

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A DYNAMIC APPROACH TO MODELING FREE TAIL COVERAGE

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  1. A DYNAMIC APPROACH TO MODELING FREE TAIL COVERAGE Robert J. Walling, ACAS, MAAA 2000 CLRS

  2. The Goal Starting With The Walker Model, Add Modifications Necessary to Reflect: 1) Current Policy Characteristics 2) Current Life Actuarial Work 3) Elements of DFA Including: a. Simulated Interest Rates b. Simulated Inflation Rates c. Simulated Mortalities

  3. Prerequisite Readings • Walker, Christopher, et al.(1996) “Death, Disability, and Retirement Coverage: Pricing the “Free” Claims-Made Tail,” Casualty Actuarial Society Forum, Winter 1996, pp. 317-346. • Society of Actuaries Group Annuity Valuation Table Task Force, Society of Actuaries Transactions, Volume XLVII, pp. 865-918. • Parmenter, Theory of Interest and Life Contingencies, 1988, Chapter 7 (Section 6 - multiple decrements). • D’Arcy, Stephen P., et al. (1997) “Building a Public Access PC-Based DFA Model,” Casualty Actuarial Society Forum, Summer 1997, Volume 2, pp. 1-40 • D’Arcy, Stephen P., et al. (1998) “Using the Public Access DFA Model: A Case Study,” Casualty Actuarial Society Forum, Summer 1998 Edition, pp. 53-118. • Ahlgrim, Kevin C., et al. (1999) “Parameterizing Interest Rate Models,” Casualty Actuarial Society Forum, Summer 1999 Edition, pp. 1-50. • A Dynamic Approach to Modeling Free Tail Coverage by Robert Walling, Casualty Actuarial Society Forum, Fall 1999

  4. Walker Approach to DD&R • Combine the effects of lapse and DD&R events to calculate the number of insureds “surviving” to the next policy term. • Estimate the premium collected for each year for the cohort adjusted to present value. • Estimate the cost of the DD&R coverage utilized at each age adjusted to present value. (Assume a relationship between the claims-made policy cost and the cost for tail coverage.) • Compute the discounted value of future DD&R losses as the sum of the discounted DD&R losses for all subsequent ages.

  5. Walker Approach to DD&R • Compute the discounted value of future DD&R premiums as the sum of the discounted DD&R premium for all subsequent ages. (Assume a selected DD&R percentage of total premium.) • The year-end unearned premium reserve is the difference between the present value of future losses and the present value of future premiums.

  6. Deterministic Enhancements • Mortality Rates Varying by Sex and Age • Waiting Periods (for DD&R Eligibility) • Varying Policy Limits • Incorporation of Historical Rate Level • Semi-retired Status.

  7. D.O.C. Insurance Company • D.O.C. Insurance Company (D.O.C.) an established writer of medical professionals practicing in a particular specialty (e.g. dentists, chiropractors, or podiatrists). They currently have 400 insureds and have data identifying each doctor according to: • Age/Date of Birth • Sex • Original Policy Inception Date • Limits of Insurance • 5 & 10 Year Waiting Periods For DD&R

  8. SOA Library of Mortality Tables • Available at www.soa.org in the Table Manager area of Actuarial File Library: • A database of 168 life insurance mortality tables • A database of 160 annuity mortality tables and projection scales • A database of 162 population mortality tables • A database of 142 versions of CSO and CET life insurance mortality tables

  9. Advantages & Disadvantages • Advantages • Following a cohort of risks through its “life cycle” is intuitive and appealing. • Still meets the NAIC level-funding requirement, but additional subsidies are identified and quantified. • More responsive to changing mortality rates. • Added precision. • Disadvantages • Still fails to reflect possible variations in mortality, loss trends and interest rates. • May add computational time • Add substantial data needs

  10. Making It Dynamic “Who of you by worrying can add a single hour to his life?” - Matthew 6:27

  11. The Dynamic Idea • Use simulation to create “environment” (interest and inflation) • Use simulation to “Kill” each doctor or cohort of doctors (The Random # of Death) • Summarize results of that simulation • Repeat several thousand times

  12. Advantages & Disadvantages • Advantages • Addresses the complexity of interest and loss inflation assumptions. • Adds variability to actual mortalities. • The stochastic simulation approach adds the ability to analyze the variability of results. • Disadvantages • Additional computational time • Significant parameter risk still exists

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