Chapter · January 998 doi: 10. 1007/978-1-4615-6187-3 10 citations reads 2,488 author: Some of the authors of this publication are also working on these related projects
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10.Retentionandcaptiveinsurance (1)
RETENTION, SELF-INSURANCE,
10 CAPTIVE INSURANCE COMPANIES Objective When insurance is available only at a high price, organizations shift from a commercial insurer to retention. This chapter identifies the nature and concept of retention and self-insurance. It reviews the factors explaining these decisions and the development of captice insurance companies.
Full coverage may not be optimal from the insurer point of view because of moral hazard and adverse selection. It may not be optimal from the insured point of view if the transaction costs are high. For example, if the expenses incurred by the insurer to settle small losses are disproportionately high, this would lead to the inclusion of a deductible in the contact that would be acceptable by the insured.
It has been demonstrated, in the case of property and liability insurance coverage, that with a loading factor k associated with the pure premium E{x} (the expected loss x), such that the premium P{x} is equal to (1+k).E{x}, full coverage cannot be optimal .
Under the expected utility approach to the problem, the individual, with an initial wealth endowment W, will agree to cover his wealth only if:
U[W] ≤ U[ W - P{x} + {x-D}] where D is a deductible.
This approach has led many authors to show that when D = 0, the optimal choice is either full coverage, or no insurance at all, depending on the size of k. It has been demonstrated that the optimal deductible will increase with the loading factor k. 1
prefers to trade some proportion of the risk for a lower insurance premium. Partial insurance means that there is some form of risk sharing defined in the insurance contract. The three most common forms are deductibles, coinsurance, and policy limits (see Chapter 8). Doherty ( 1985, Chap. 12) examined the 2
composite financial strategies involving these risk sharing arrangements. A deductible is generally considered to be more efficient than a proportionate sharing device such as coinsurance because it releases both the insurer and the insured from settlement expenses.
In life insurance contracts, no monetary deductible is available (although some form of time deductible or waiting period may exist) but the theory of partial insurance still applies if we make the reasonable assumption that an individual never buys coverage for the full value of his human life. Therefore, in this case, a special form of coinsurance, with no penalty, should be considered as the risk sharing arrangement. 2
______________________________________________________ DISCUSSION: Relatively large deductibles are generally preferred by firms to avoid settlement expenses for small losses that can easily be budgeted. The effect of a deductible on the loss distribution limits the severity of the losses but does not affect the frequency. The larger the deductible, the larger will be the premium reduction because the probability for small losses is usually much higher than for large losses.
Example: The information concerning the frequency and severity distributions for BEST-RENT-A-CAR Company (Chap. 5) is used to estimate the pure premium. Assuming a per-occurence deductible, the pure premium method gives the following results:
With no deductible, pure premium = 0.4 x 1,900 = $760 With a deductible of $1,000 = 0.4 x 1,600 = $640
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= 0.4 x 600 = $240
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