14.1 Introduction

Definition 14.1 Premium Asset (3 definitions)

  • On retrospectively rate policies, premium that the insurer expects to collect based on the expected ultimate loss experience less the premium that the insurer has already booked, or

  • Earned But Not Reported Premium (EBNR) ,or

  • Asset supported by premium the insurer expect to collect from clients with retrospective policies as losses develops

Remark. Admitted portion of the premium asset appears on the balance sheet as the “Asset for Accrued Retrospective Premiums”

Background: Retrospective policies were popular in 1996:

  • For insured:

    • Returns premium to insured for good experience

    • Cashflow: Premiums are due with short lag to losses, as opposed to upfront

  • For insurer:

    • Allows insurer to attracts good customers that expect to see favorable loss experience through loss control and loss management

    • Allows an insurance company to shift a significant portion of the risk to the insured

      (Uncertainty due to inflation, rate regulations, uncertainty in claims compensation, increase utilization of the insurance benefits, growing attorney involvement)

Estimating the premium asset was needed for many commercial lines insurers as this asset frequency exceeds 10% of surplus

14.1.1 Discussion of Berry and Fitzgibbon Method

Method for calculating retro reserve [Premium deviation to date] - [Ultimate premium deviation]

Definition 14.2 \[\dfrac{\text{Ultimate Premium}}{\text{Standard Premium}}\]

Ultimate Premiums Deviation: Amount by which the ultimate premium for a retro rated policy is expected to differ from the standard premium (manual premium w/ adj for experience)

Premium deviation to date: Amount by which the currently booked premium differs from the standard premium

Fitzgibbon Method:

  1. Analyze the historical relationship between the loss ratio and the premium deviation using statistical techniques

  2. Apply the relationship to the projected loss ratio to calculate the projected ultimate premium deviation

  3. Retro reserve = [Ultimate premium deviation] - [Premium deviation to date]

Berry Method:

  1. Estimate ultimate premium with historical premium emergence pattern

  2. Subtract estimated ultimate premium by current premium

Caveat: Lack intuitive appeal

  • Methods do not consider how a retro rating formula actually works

  • i.e. premium is a function of loss, with retro rating parameters such as the loss conversion factor, tax multiplier, retro min/max

\(\therefore\) Premium asset should be establish as a function of reported loss and the reserve for loss development

  • Where the function is defined by the retro rating parameters