Casualty Actuarial Society


Proposed Research Project on Risk Adjustments for Discounting

CAS Theory of Risk Committee

Researcher(s) Wanted for Proposed Research Project on Risk Adjustments for Discounting

  1. Casualty Actuarial Society (CAS)

    The CAS was organized in 1914 as a professional society with the purpose of advancing the body of knowledge of actuarial science applied to property, casualty and similar risk exposures. This is accomplished through communication with the publics affected by insurance, the presentation and discussion of papers, attendance at seminars and workshops, collection of a library, research, and other means. The membership of the CAS includes over 3,000 actuaries employed by insurance companies, industry advisory organizations, national brokers, accounting firms, educational institutions, state insurance departments, the federal government and independent consultants.

  2. Theory of Risk Committee (COTOR)

    The Theory of Risk Committee is charged with developing and demonstrating the utility of specific applications of the theory of risk to various lines of property and casualty insurance. The COTOR is sponsoring this research on behalf of the CAS.

  3. CAS Interest in the Subject

    The topic of the appropriate procedure to account for risk in discounted loss reserves and its counterpart in the discounted loss portion of premiums has been the subject of research and discussion in the actuarial profession for many years. A number of procedures have been presented in the literature, with some authors having strong opinions on the subject. An approach integrating the various approaches of the previous researchers and advancing the state of the art would be an important step in providing guidance to practicing actuaries and regulators.

  4. Statement of the Problem

    The discounted expected value of losses and associated expenses is an actuarial estimate of uncertain values, i.e., a random variable, of the losses and associated expenses to be paid in a future time period that is calculated to reflect the time value of money. Such losses and expenses may be those associated with a future policy period, an unexpired policy period (unearned premium), or unresolved or unreported claims for events which have already taken place (outstanding case reserves and IBNR).

    The calculation of "risk adjusted" discounted losses and expenses is intended to combine the expected value of losses and expenses, the discounted "present value" adjustment for the time value of money, and a "risk adjustment" for the risks associated with the uncertainties underlying the values of losses and expenses, the timing of the payments, and the rates used for discounting. It is generally agreed that the purpose of risk adjustments is to increase the value of the discounted losses and expenses because they represent obligations to be satisfied by future uncertain payments. The methods used to calculate risk adjustments for discounted losses are not thought to be independent of the methods used for computing the discounted present value of losses. Some view the difference between undiscounted and discounted values as an appropriate risk adjustment or "risk margin". Others believe that a risk adjusted discount rate, smaller that the non-adjusted rate, should be used to calculate the risk adjusted expected discounted losses and expenses.

    The COTOR is seeking qualified researchers to conduct a research project that addresses the following question: How should actuarially appropriate risk adjustments be computed when losses and expenses are discounted?

  5. Project Outline
    1. Literature Survey: The research should include a comprehensive survey of the literature from actuarial, as well as financial and any other relevant sources, for any research relating to this issue. The researcher will be expected to compile a bibliography of such research.

      Interested researchers can review a Summary of the Literature on risk adjusted discount rates prepared by the COTOR. The summary can be downloaded from the CAS Web Site at

    2. Risk Adjustment Procedures: The research project will include the development of one or more procedures for determining how to adjust for risk when discounting property and casualty losses and expenses. The goal of such procedures is to synthesize the relevant views from actuarial, financial and statistical literature in keeping with accepted theories and principles concerning risk in financial valuations. The procedure(s) should explicitly address the treatment of process risk and parameter risk. Other sources of risk can also be addressed. The procedure(s) should be presented in a form that can be implemented in a practical manner. The development of software may be required in the scope of the project if the procedures are otherwise difficult to implement.

    3. The project will include writing a paper, suitable for publication in the CAS Proceedings, that presents the conclusions of the research and the risk adjustment procedure(s).

    4. Detailed Examples: The project may include the development of sample applications of the procedure(s) to:
      1. Loss and loss expense reserves.
      2. Estimated future losses and expenses (or premium).
      3. Unearned premium reserves.
      4. Both fast and slow payment patterns.
    5. The project may include a comparison of the proposed procedure(s) with those of others cited in the survey from section a.

    6. The project may include a review of the implications of the procedure(s) with respect to the determination of risk-based capital and the actuarial pricing of insurance.

  6. Research Funding

    Funding for this research is principally through the CAS but may include other research funding organizations. The amount of funds available for this project has not been determined at this time. The final scope of the project will be decided by the committee based on the research costs for various items and the expected results of the project.

  7. Researcher Qualifications

    Interested researchers should submit their resumes (if a firm, of the principal individual(s) performing or directing the work), indicating how their background, education, and experience bear on their qualifications to undertake this research. Specifically, researchers should specify their qualifications and expertise to perform research in the application of finance, statistics and actuarial theories to insurance problems. Researchers should indicate their relevant work or research experience and professional accomplishments (e.g., papers published). Researchers should also supply one or two paragraphs of discussion outlining how they would approach the problem.

    The CAS will select the researcher or researchers who, in the judgment of the COTOR and on the basis of his or her qualifications and expertise, is best able to perform the research project as outlined above. If the COTOR determines that no researcher is suitably qualified to perform this research project, then no contract will be awarded.

    Interested researchers should submit their qualifications and any questions in writing to:

    Louise Francis
    Casualty Actuarial Society
    1100 N. Glebe Road, Suite 600
    Arlington, VA 22201
    Phone: (703) 276-3100
    Fax: (703) 276-3108

    Receipt of submissions will be acknowledged. Members of a subcommittee of the COTOR will evaluate the researchers' qualifications. The current membership of the COTOR includes:

    Rodney E. Kreps, Chairperson

    Richard R. Anderson

    Nasser Hadidi

    John G. Aquino

    Leigh Joseph Halliwell

    Ward M. Brooks

    Philip E. Heckman

    Robert J. Finger

    Charles N. Kasmer

    Louise A. Francis

    Donald F. Mango

    James R. Garven

    Glenn G. Meyers

    William R. Gillam

    Stephen J. Mildenhall

    Farrokh Guiahi


  8. Schedule

    April 1, 1999

    Researcher qualifications due to committee.


    April 30, 1999

    Researcher selection by the COTOR.


    June 30, 1999

    Progress reports are due to the oversight committee.

    September 30, 1999


    December 31, 1999


    February 28, 2000


    March 30, 2000

    Final research is due.

  9. Presentation, Ownership and Publication of Report

    If asked, the researcher(s) agree to be available to present the report at a CAS meeting or seminar. If travel is required, reasonable expenses will be paid in addition to the compensation provided in the research contract.

    As a condition of selection, the CAS requires that all right, title, and interest, including copyright and patent, in and to the report be owned by the CAS. The selected researcher(s) must sign a formal Agreement (attached) that assigns all such rights to the CAS. Of course, in any publication of the report, the researcher(s) will be given appropriate credit. The CAS intends to submit the report to the CAS Committee on Review of Papers for consideration as a CAS Proceedings paper. Alternately, the CAS may publish the research in the CAS Forum.

    Guidelines for submitting papers for publishing in the CAS Proceedings are as stated on the CAS Web Site at, and in the CAS Yearbook.

  10. Additional Information (attached)

    Consulting Agreement