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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.
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.
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 or development [1] method is a prominent [2] [3] actuarial loss reserving technique. The chain-ladder method is used in both the property and casualty [1] [4] and health insurance [5] fields. Its intent is to estimate incurred but not reported claims and project ultimate loss amounts. [5]
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.
Reserves created from profit, especially retained earnings, i.e. accumulated accounting profits, or in the case of nonprofits, operating surpluses. [3] However, profits may be distributed also to other types of reserves, for example: legal reserve fund from profit - many legislations require creation of the fund as a percentage of profits
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From this we can see that the present value of the loss to the insurance company now if the person dies in t years, is equal to the present value of the death benefit minus the present value of the premiums. The loss random variable described above only defines the loss at issue. For K(x) > t, the loss random variable at time t can be defined as: