Loss reserving refers to the calculation of the required reserves for a
tranche of general
insurance business.
[Schmidt, K. D., Zocher, M.]
The Bornhuetter–Ferguson Principle
Variance 2:1, 2008, pp. 85-110. It includes outstanding claims reserves.
Typically, the claims reserves represent the money which should be held by the insurer so as to be able to meet all future
claims arising from policies currently in force and policies written in the past.
Methods of calculating reserves in
general insurance are different from those used in
life insurance
Life insurance (or life assurance, especially in the Commonwealth of Nations) is a contract between an insurance policy holder and an insurer or assurer, where the insurer promises to pay a designated beneficiary a sum of money upon the death ...
,
pension
A pension (, from Latin ''pensiō'', "payment") is a fund into which a sum of money is added during an employee's employment years and from which payments are drawn to support the person's retirement from work in the form of periodic payments ...
s and
health insurance
Health insurance or medical insurance (also known as medical aid in South Africa) is a type of insurance that covers the whole or a part of the risk of a person incurring medical expenses. As with other types of insurance, risk is shared among ma ...
since general insurance contracts are typically of a much shorter duration. Most general insurance contracts are written for a period of one year, and typically there is only one payment of
premium at the start of the contract in exchange for coverage over the year. Reserves are calculated differently from contracts of a longer duration with multiple premium payments since there are no future premiums to consider in this case. The reserves are calculated by forecasting future losses from past losses.
Methods
The most popular methods of claims reserving include the
chain-ladder method and the
Bornhuetter–Ferguson method.
Another method is frequency-severity approach, used mainly when data is sparse.
The
chain-ladder method, also known as the development method, assumes that past experience is an indicator of future experience.
Loss development patterns in the past are used to estimate how claim amounts will increase (or decrease) in the future.
The Bornhuetter–Ferguson method uses both past loss development as well as an independently derived prior estimate of ultimate expected losses.
Outstanding claims reserves
Outstanding claims reserves in
general insurance are a type of
technical reserve
Technical may refer to:
* Technical (vehicle), an improvised fighting vehicle
* Technical analysis, a discipline for forecasting the future direction of prices through the study of past market data
* Technical drawing, showing how something is co ...
or accounting
provision in the
financial statements of an insurer. They seek to quantify the 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.
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 modeled as
random variables
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the po ...
. In general, there is a delay in the insurer's settlement of the claim. Typical reasons for this are: (i) reporting delay (time gap between
claims occurrence and claims reporting at the insurance company) and; (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
[Wüthrich, M.V., Merz, M., ''Stochastic Claims Reserving Methods in Insurance'', Wiley Finance, 2008, Section 1.1.]
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
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For example, the average of the numbers 2, 3, 4, 7, ...
methods
*
Bornhuetter–Ferguson method
* Paid-incurred chain (PIC) claims reserving model
* Bootstrap methods
* Bayesian methods
Most of these methods started off as ''deterministic'' algorithms. Later actuaries started to develop and analyze underlying stochastic models that justify these algorithms. The most popular stochastic model is probably the distribution-free chain ladder method, which was developed by T. Mack. These stochastic methods allow one 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).
[England, P.D., Verrall, R.J., ''Stochastic claims reserving in general insurance'', British Actuarial Journal 8/3, 443-518, 2002.]
See also
*
Incurred but not reported
*
Chain-ladder method
*
Bornhuetter–Ferguson method
*
Actuarial science
References
Bibliography
*Meyers, Glenn G., Stochastic Loss Reserving Using Bayesian MCMC Models
CAS Monograph No. 1. 2015
*Meyers, Glenn G., Stochastic Loss Reserving Using Bayesian MCMC Models (2nd Edition)
CAS Monograph No. 8. 2019
Actuarial science