A dynamic approach to modeling free tail coverage
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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