Outstanding claims reserves

Outstanding claims reserves in general insurance are a type of technical reserve or accounting provision in the financial statements of an insurer. They seek to quantify the outstanding loss liabilities for insurance claims which have been reported and not yet settled (RBNS) or which have been incurred but not yet reported (IBNR) reserves. This is a technical reserve of an insurance company, and is established to provide for the future liability for claims which have occurred but which have not yet been settled.

Background

An insurance policy provides, in return for the payment of a premium, acceptance of the liability to make payments to the insured person on the occurrence of one or more specified events (insurance claims) over a specific time period. The occurrence of the specified events and the amount of the payment are both usually modelled as random variables. In general, there is a delay in the insurer's settlement of the claim, typical reasons are (i) reporting delay (time gap between claims occurrence and claims reporting at the insurance company); (ii) settlement delay because it usually takes time to evaluate the whole size of the claim. The time difference between claims occurrence and claims closing (final settlement) can take days (e.g. in property insurance) but it can also take years (typically in liability insurance).

Claims reserving now means, that the insurance company puts sufficient provisions from the premium payments aside, so that it is able to settle all the claims that are caused by these insurance contracts. This is different from social insurance where one typically has a pay-as-you-go system which means that premium payments are not matched to the contracts that cause the claims, see Wüthrich-Merz (2008), Section 1.1.Claim payments are generally normally distributed ~N(0,1)

Method of estimation

Various statistical methods have been established for the calculation of outstanding claims reserves in general insurance. These include:

• Distribution-free chain-ladder method
• Over-dispersed Poisson (ODP) model
• Hertig's log-normal chain ladder model
• Separation method
• Average cost per claim methods
• Bornhuetter-Ferguson method
• Paid-incurred chain (PIC) claims reserving model
• Bootstrap methods
• Bayesian methods

(see Benjamin (1987), Taylor (2000), England-Verrall (2002) and Wüthrich-Merz (2008))

Most of these methods started off as deterministic algorithms. Later actuaries started to develop and analyze underlying stochastic models that justify these algorithms. Probably, the most popular stochastic model is the distribution-free chain ladder method which was developed by T. Mack (1993). These stochastic methods allow to analyze and quantify the prediction uncertainty in the outstanding loss liabilities. Classical analysis studies the total prediction uncertainty, whereas recent research (under the influence of Solvency 2) also studies the one-year uncertainty, called claims development result (CDR), see Merz-Wüthrich (2008). England-Verrall (2002) and Wüthrich-Merz (2008) provide good overviews.

References

• Benjamin, B., General Insurance, Heinemann, 1987, London.
• England, P.D., Verrall, R.J., Stochastic claims reserving in general insurance, British Actuarial Journal 8/3, 443-518, 2002.
• Mack, T., Distribution-free calculation of the standard error of chain ladder reserves estimates, ASTIN Bulletin 23/2, 213-225, 1993.
• Merz, M., Wüthrich, M.V., Modelling the claims development result for solvency purposes, CAS E-Forum, Fall 2008, 542-568, 2008.
• Meyers, Glenn G., Stochastic Loss Reserving Using Bayesian MCMC Models, CAS Monograph No. 1. 2015.
• Taylor, G., Loss Reserving: An Actuarial Perspective, Kluwer, 2000, Boston.
• Wüthrich, M.V., Merz, M., Stochastic Claims Reserving Methods in Insurance, Wiley Finance, 2008.