Run of triangles is also called Run of triangles is also called delay triangles is used to delay triangles is used to

estimate the total premium estimate the total premium amount and reserve amount amount and reserve amount on the basis of the projected on the basis of the projected

claim amount and claim claim amount and claim numbers.numbers.

•Basic Chain Ladder MethodBasic Chain Ladder Method•adjusted chain ladder methodadjusted chain ladder method•Average cost per claim methodAverage cost per claim method•Bornhuetter-ferguson methodBornhuetter-ferguson method

•Run-off triangles usually arise Run-off triangles usually arise particularly in non life insurance .particularly in non life insurance .

•It is important that the claims It is important that the claims are attributed to the year in are attributed to the year in which the accident occurred.which the accident occurred.

•The insurance company needs The insurance company needs to know how much it is liable to to know how much it is liable to pay in claims so that it can pay in claims so that it can calculate how much surplus it calculate how much surplus it has to made. has to made.

1.1. IBNR (Incurred but not IBNR (Incurred but not reported)reported)

2.2. Outstanding reportedOutstanding reported

• IBNR (Incurred but not IBNR (Incurred but not reported) i.e the claim event reported) i.e the claim event has occurred, but has not yet has occurred, but has not yet been reported to the insurer.been reported to the insurer.

• An outstanding reported An outstanding reported claims have been reported , claims have been reported , but have not yet been closed.but have not yet been closed.

The normal steps involved in settling a The normal steps involved in settling a general insurance claim :general insurance claim :

Question:-

Identify where each of these reserves fits in on the diagram above.

•Claims data will be presented Claims data will be presented as a triangle , which is the most as a triangle , which is the most commonly used method .commonly used method .

•The year in which the incident The year in which the incident happened and the insurer was on happened and the insurer was on risk is called the accident year.risk is called the accident year.

•The number of years until a The number of years until a payment is made is called the payment is made is called the development year.development year.

•Claims data may be presented Claims data may be presented cumulatively , or on an individual cumulatively , or on an individual basis. basis.

•Each entry, Cij , in the run-off triangle can be expressed in general termsCij = rj . si . xi+j + eij whererj is the development factor for year j, representing theproportion of claim payments by year j. Each rj isindependent of the origin year i.si is a parameter varying by origin year, i, representing theexposure, for example the number of claims incurred in theorigin year i.xi+j is a parameter varying by calendar year, for examplerepresenting inflation.eij is an error term.

•Each entry in the table can be defined by its origin year (row) and its development year (column)

•The figure of 2216 is for origin year 2001, Development year 2

• we will write as 2001/2 orC2001,2

•The task is to decide the The task is to decide the amounts yet to be paid in respect amounts yet to be paid in respect of the given accident year.of the given accident year.

•The process to fill in the lower The process to fill in the lower triangle by comparing present triangle by comparing present figures with past experience is figures with past experience is the main object.the main object.

•The basic assumption made in The basic assumption made in estimating out standing Claims estimating out standing Claims concerns the run off pattern .concerns the run off pattern .

•The simplest assumption is that The simplest assumption is that payment will emerge in a similar way payment will emerge in a similar way in each accident year.in each accident year.

•The ratio that are used to project The ratio that are used to project future claims are known as future claims are known as development factorsdevelopment factors

For each accident year from 2001 to 2004 there is a different ratio for the increase in cumulative payments from development year 0 to development year 1. It is not clear which is the “correct” one to use when projecting forward foraccident year 2005. For a conservative estimate of cumulative payments, it might be best to take the largest ratio, ie 1.823.

This suggests using a weighted average and the usual choice of weights are thecumulative claims values.

This method of estimating the ratios which describe the run-off pattern is calledthe chain-ladder method.

•In this section we will carry out the In this section we will carry out the calculations for completing the run of calculations for completing the run of triangle using the basic chain ladder triangle using the basic chain ladder method.method.

•The name given to this method The name given to this method presumably arises from the ladder presumably arises from the ladder like operations which are chained like operations which are chained over the development year.over the development year.

•The chain ladder method can also The chain ladder method can also be applied to a triangle of loss ratio be applied to a triangle of loss ratio data rather than cumulative data rather than cumulative payments. payments.

•The ratio of incurred claims to The ratio of incurred claims to earned premiums over a defined earned premiums over a defined period is called the loss ratio. period is called the loss ratio.

•A loss ratio is based on trends of A loss ratio is based on trends of past data, under-writers views, or past data, under-writers views, or market data ,could be used as a market data ,could be used as a basis for an estimate of the eventual basis for an estimate of the eventual loss and hence the outstanding loss and hence the outstanding claims.claims.

•The chain ladder technique is used The chain ladder technique is used primarily to estimate the primarily to estimate the development claim payments.development claim payments.

•However, it is useful to check However, it is useful to check whether it fits reasonably with the whether it fits reasonably with the claims data which have already been claims data which have already been received.received.

•It is possible to adjusted the It is possible to adjusted the claculated development factors in claculated development factors in the light of other information.the light of other information.

•The development factors, either The development factors, either calculated directly from the data, or calculated directly from the data, or set using expert knowledge ,are set using expert knowledge ,are always used in the same way to always used in the same way to estimate outstanding claim estimate outstanding claim payments.payments.

•The chain ladder technique is based The chain ladder technique is based on the assumption that payments on the assumption that payments from each accident year will develop from each accident year will develop in the same way. in the same way.

•The final assumption made when The final assumption made when the chain ladder technique is used the chain ladder technique is used concerns inflation.concerns inflation.