Casualty Actuarial Society

Press Room

Request for Proposals for Predictive Modeling Methods in Ratemaking

02/21/2018 —

  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 4,000 actuaries employed by insurance companies, industry advisory organizations, national brokers, accounting firms, educational institutions, state insurance departments, the federal government, and independent consultants.
  2. Committee on Ratemaking
    The CAS Committee on Ratemaking  (Ratemaking Committee) is charged with facilitating research and providing direction, guidance, and support to the profession, regulators, and others regarding ratemaking for property & casualty risks.  The Ratemaking Committee will sponsor the research to be conducted under this Request for Proposal (‘RFP’) on behalf of the CAS.
  3. CAS Interest in the Subject
    The CAS has recently made it a strategic goal to further the education and skills of actuaries in the area of predictive modeling.  One of the keys to furthering these goals is through funding research in predictive modeling within actuarial science. 

    Generalized linear models (GLMs) were first introduced in the 80s, which helped to spawn a wave of techniques predicting future uncertain outcomes and assessing correlations between covariates and a given outcome.  While this set of techniques goes by many names, the CAS collectively refers to them as predictive modeling.  Over the past 20 years, GLMs have been introduced in the P&C insurance industry for developing risk classification systems and have become the recommended technique as a starting point for said development.  However, even with the standardization of GLMs for risk classification systems, actuarial research in the use of predictive modeling has been sparse when it comes to predictive modeling techniques beyond GLMs.
  4. Research Problem Description
    Prior to the advent of GLMs for use in developing risk classification systems, credibility methods were the standard for estimating the parameters prescribed by actuaries for use in risk classification systems.  Part of the reason why GLMs were so different from actuarial credibility methods was due to the difference in a fundamental assumption the two methods made about the risk characteristics in the classification systems.  Namely, credibility assumes the risk characteristics are random effects whereas GLMs assume these are fixed effects (see, Ohlsson and Klinker).  Given that both methods have preferable properties in certain situations, several approaches have been posited for directly combining the two (again, see Ohlsson and Klinker), as well as indirect combinations (see, Miller and Frees).  The Ratemaking Committee would like an investigation into which of these methods would be most desirable for practical purposes.
  5. Project Requirements
    The Ratemaking Committee requests proposals from qualified researchers to use a single data set to produce a research document discussing a preferred approach for combining GLM and credibility methods.

    Specific methods that must be investigated:


    1. Generalized Linear Models,
    2. At least one of the implementations of mixed effect models as proposed by Ohlsson or Klinker; and,
    3. Generalized Linear Models with Penalty term (aka, shrinkage or regularization )

    Additional aspects of the research that must be explicitly addressed in the research document:
    1. High level discussion of the theoretical properties of each method under investigation and any desirable or undesirable aspects thereof and potentially how these relate to the research findings,
    2. Comparison of any difficulties in convergence of the methods investigated,
    3. For b, above, discussion of how to select which risk characteristics should be treated as fixed effects and for c, whether any risk characteristics should be left out of the regularization term,
    4. For c, above, discussion of how to choose the best hyperparameter for the penalty term,
    5. Comparison of the processing times required to arrive at model convergence for the methods investigated,
    6. Comparison of the parameter estimates resulting from the methods investigated,
    7. Comparison of the performance for the methods investigated on holdout data,
    8. Discussion of the recommended method, if any clear one exists, as based on results from ii and v-vii, above.

    The Ratemaking Committee would like to issue an RFP to that effect for a fee not to exceed $25,000.

    Ohlsson, E., and B. Johansson, “Combining Credibility and GLM for Rating of Multi-Level Factors,” CAS Discussion Paper Program, 2004, pp. 315-326.

    Ohlsson, E., “Credibility Estimators in Multiplicative Models,” Research Report 2006:3, Mathematical Statistics Stockholm University.

    Ohlsson, E., “Combining Generalized Linear Models and Credibility Models in Practice,” Scandinavian Actuarial Journal, 2008, 4, 301-314.

    Klinker, Fred (2010).  “Genearlized Linear Mixed Models for Ratemaking: A Means of Introducing Credibility into a Generalized Linear Model Setting”, Casualty Actuarial Society, E-Forum, Winter 2011-Volume 2. 

    Tibshirani, Robert (1996). "Regression Shrinkage and Selection via the lasso". Journal of the Royal Statistical Society. Series B (methodological). Wiley. 58 (1): 267–88. JSTOR 2346178.

    Miller, Hugh, “A discussion on credibility and penalised regression, with implications for actuarial work”, Prepared for the Actuaries Institute 2015, ASTIN, AFIR/ERM and IACA Colliquia, August 2015.

    Frees, Edward W., and Gee Lee, “Rating Endorsements Using Generalized Linear Models”, Variance, 10:1, 2016, pp. 51-74.

    Project Schedule (Details negotiable)

    February 20, 2018 - Publish RFP
    March 20, 2018 – Proposals due
    April 20, 2018 - Final selection of research team
    July 15, 2018 - First draft due
    September 21, 2018 - Final draft due
    October 26, 2018 - Final Report produced and approved by Ratemaking Committee
  6. Proposal Requirements
    Proposals should include:
    • A clear outline of the work that will be performed and the time frame in which it will be performed (including key dates). The more specific the proposal covers the goals the better.  
    • An estimate of expected costs. Cost estimates should be itemized and specifically note the estimated costs for cloud compute resources, to the extent the respondent intends to use such resources.
    • Description of the data intended to be used and the selected dependent variable(s).
    • A catalog of all software languages intended to be used (R, Python, etc) and libraries, if applicable.
    • Descriptions of the algorithms intended to be used, including identification of which algorithms from Ohlsson and Klinker will be used, as well as the particular type(s) of penalty term(s) that will be used in combination with the GLM. 
    • Specific reference to the extent to which the researcher(s) intends to be coding the algorithms from scratch versus relying on pre-existing code, and if the latter, the pre-existing code intended to be used.
    • The model performance tests intended to be used on holdout data.
    • The proposal should be accompanied by the resumes of the researcher(s), indicating how their background, education, and experience bear on their qualifications to undertake the review.

    Receipt of proposals will be acknowledged in a timely manner. All decisions regarding the evaluation of responses to the RFP will be awarded entirely based on the information provided in the written proposals.  The CAS will award the contract to the respondent who, in the judgment of the Ratemaking Committee, is best able to perform the work as specified herein.  If it is determined that no proposal meets the requirements of the RFP, then no contract will be awarded. When a respondent is chosen by Ratemaking Committee and the contract awarded, respondents not awarded the contract will be so informed shortly thereafter. Interested researchers should submit their proposals and any questions in writing to:

    Casualty Actuarial Society
    Attention: Karen Sonnet, RFP Ratemaking
    4350 N. Fairfax Dr. Suite 250
    Arlington, VA 22203
    Phone: (703) 276-3100 ext. 762

  7. 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 Section 5.

    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 must sign a formal Agreement (attached) that assigns all such rights to the CAS. Of course, in any publication of the report, the researcher will receive appropriate credit. The CAS may publish the report in any CAS publication, including electronic versions such as on its Web site or on compact discs.

Back to All News Articles

Back to Future-Fellows News