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: a. Simulated Interest Rates b. Simulated Inflation Rates c. Simulated Mortalities

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 Society of Actuaries Group Annuity Valuation Table Task Force, Society of Actuaries Transactions, Volume XLVII, pp 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 D’Arcy, Stephen P., et al. (1998) “Using the Public Access DFA Model: A Case Study,” Casualty Actuarial Society Forum, Summer 1998 Edition, pp Ahlgrim, Kevin C., et al. (1999) “Parameterizing Interest Rate Models,” Casualty Actuarial Society Forum, Summer 1999 Edition, pp A Dynamic Approach to Modeling Free Tail Coverage by Robert Walling, Casualty Actuarial Society Forum, Fall 1999

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&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 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.) 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 Available at 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 –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 “Who of you by worrying can add a single hour to his life?” - Matthew 6:27

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 & 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