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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

A DYNAMIC APPROACH TO MODELING FREE TAIL COVERAGE

Robert J. Walling, ACAS, MAAA

2000 CLRS

the goal
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

prerequisite readings
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
walker approach to dd r
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.
walker approach to dd r1
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.
deterministic enhancements
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.
d o c insurance company
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
soa library of mortality tables
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
advantages disadvantages
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
making it dynamic
Making It Dynamic

“Who of you by worrying can add a single hour to his life?”

- Matthew 6:27

the dynamic idea
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
advantages disadvantages1
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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