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For example, when a claim is first reported, a $100 payment might be made, and a $900 case reserve might be established, for a total initial reported amount of $1000. However, the claim may later settle for a larger amount, resulting in $2000 of payments from the insurer to the claimant before the claim is closed.
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Loss reserving is the calculation of the required reserves for a tranche of insurance business, [1] including 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.
The chain-ladder technique is only accurate when patterns of loss development in the past can be assumed to continue in the future. [ 1 ] [ 3 ] [ 4 ] In contrast to other loss reserving methods such as the Bornhuetter–Ferguson method , it relies only on past experience to arrive at an incurred but not reported claims estimate.
For insurance, the loss ratio is the ratio of total losses incurred (paid and reserved) in claims plus adjustment expenses divided by the total premiums earned. [1] For example, if an insurance company pays $60 in claims for every $100 in collected premiums, then its loss ratio is 60% with a profit ratio/gross margin of 40% or $40.
Ultimate loss amounts are necessary for determining an insurance company's carried reserves. They are also useful for determining adequate insurance premiums, when loss experience is used as a rating factor [4] [5] [6] Loss development factors are used in all triangular methods of loss reserving, [7] such as the chain-ladder method.
where is the maturity of the longest transaction in the portfolio, is the future value of one unit of the base currency invested today at the prevailing interest rate for maturity , is the loss given default, is the time of default, () is the exposure at time , and (,) is the risk neutral probability of counterparty default between times and .
The Bornhuetter–Ferguson method was introduced in the 1972 paper "The Actuary and IBNR", co-authored by Ron Bornhuetter and Ron Ferguson. [4] [5] [7] [8]Like other loss reserving techniques, the Bornhuetter–Ferguson method aims to estimate incurred but not reported insurance claim amounts.