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Nature & Functions of Insurance

In its simplest aspect, insurance has two fundamental characteristics:

1. Transfer of risk from the individual to the group.

2. Sharing of losses on some equitable basis.

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Operation of Insurance Illustrated

1. 1,000 dwellings valued at $100,000 each.

2. Each owner faces risk of a $100,000 loss.

3. Owners agree to share losses that occur.

4. If one house burns (total loss) each owner pays $100 ($100 X 1,000 = $100,000).

5. This is a pure assessment mutual insurance plan.

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Operation of Insurance (continued)

6. Potential difficulty: some members might refuse to pay their assessment.

7. This problem can be overcome by requiring advance payment for predicted future losses (based on past experience).

8. If 2 total losses are predicted, each owner’s cost is $200.

9. If we add $100 for a cushion and for operating expenses, the cost is $300.

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Insurance Defined: Individual Perspective

Insurance is an economic device whereby the individual substitutes a small certain cost (the premium) for a large uncertain financial loss (the contingency insured against) which would exist if it were not for the insurance.

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Risk Reduction Through Pooling

1. The risk an insurer faces is not merely a summation of risks transferred to it by individuals.

2. Insurer can predict within narrow limits the amount of losses that will occur.

3. If insurer could predict future losses with absolute precision, it would have no risk.

4. Accuracy of insurer’s prediction is based on the law of large numbers.

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Probability Theory and Law of Large Numbers

Probability theory is the body of knowledge concerned with measuring the likelihood that something will happen and making predictions based on this likelihood.

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Probability Theory and Law of Large Numbers

1. Likelihood of an event is assigned a numerical value between 0 and 1.

2. Impossible events assigned a value of 0.

3. Inevitable events assigned value of 1.

4. Events that may or may not happen are assigned a value between 0 and 1, with higher values assigned to those with greater likelihood.

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Two Interpretations of Probability

1. Relative frequency interpretation• signifies the relative frequency of

occurrence that would be expected, given a large number of separate independent trials.

2. Subjective interpretation• probability is measured by the degree of

belief (e.g., student says she has a 50:50 chance of getting a B in the course).

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Determining the Probability of an Event

1. A priori estimates determined from the underlying conditions• the probability of flipping a “head” is .5• the probability of drawing the Ace of

Spades is 1/52

2. A priori estimates not significant for us except in illustrating Law of Large Numbers

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Law of Large Numbers

1. Even though we know the probability of “head” is .5, we know we cannot predict whether a given flip will be a head or a tail.

2. Given a sufficient number of “flips,” we would expect the result to approach one-half “heads” and one-half “tails.”

3. This common sense notion that probability is meaningful only over a large number of trials is recognition of the Law of Large Numbers.

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Law of Large Numbers

The observed frequency of an event more nearly approaches the underlying probability of the population as the number of trials approaches infinity.

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A Posteriori Probabilities

1. When probability cannot be determined by underlying conditions (i.e., a priori), it can be estimated based on past experience.

2. A posteriori probabilities are based on observed frequencies of past events.

3. After observing proportion of the time that various outcomes occur, we construct an index of relative frequencies of occurrence called a probability distribution.

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Probability Distribution

1. Probability distribution is an index of the relative frequency of all outcomes.

2. The probability assigned to the event is the average rate at which the outcome is expected to occur.

3. Probability distributions generally constructed on basis of a sample.

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Illustration of Sampling of Losses

Year Houses that Burn

1 72 113 104 95 13

Total 50

Average 10

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Illustration of Sampling of Losses

Year Houses that Burn

1 162 43 104 125 8

Total 50

Average 10

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Standard Deviation

Average Actual DifferenceYear Losses Losses Difference Squared

1 10 7 3 92 10 11 1 13 10 10 0 04 10 9 1 15 10 13 3 920

Summation of Differences Squared = 20 = 4 Number of Years 5

Variance = 4, Standard Deviation = 2

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Standard Deviation

Average Actual DifferenceYear Losses Losses Difference Squared

1 10 16 6 362 10 4 6 363 10 10 0 04 10 12 2 45 10 8 2 480

Summation of Differences Squared = 80 = 16 Number of Years 5

Variance = 16, Standard Deviation = 4

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Significance of Standard Deviation

1. The smaller the standard deviation relative to the mean, the less the dispersion of the values in the population.

2. In our example, if a large number of samples were taken, 68.27% of the means (of the samples) would fall between 10 + the standard deviation.

3. For the first set of data, 10 + 2.

4. For the second set, 10 + 4.

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Dual Application of Law of Large Numbers

1. To estimate the underlying probability accurately, insurer must have a large sample of experience.

2. Once the estimate of probability has been made, it must be applied to a large number of exposure units to permit the underlying probability “to work itself out.”

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Insurance Defined Social Perspective

Insurance is an economic device for reducing and eliminating risk through the process of combining a sufficient number of homogeneous exposures to make the losses predictable for the group as a whole.

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Insurance: Transfer or Pooling?

1. The view that the essence of insurance is risk transfer emphasizes the individual’s substitution of a small small certain cost for large uncertain loss.

2. Emphasis on pooling or risk sharing emphasizes the role of reducing risk in the aggregate.

3. Insurance can exist without pooling, but not without transfer.

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Insurance and Gambling

1. In gambling, there is no chance of loss (and therefore no risk) prior to the wager.

2. In the case of insurance, the chance of loss exists whether or not insurance is purchased.

3. Gambling creates risk, while insurance provides for the transfer of existing risk.

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Economic Contribution of Insurance

1. Creates certainty about burden of loss

2. Spreading losses that do occur

3. Provides for an optimal utilization of capital

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Elements of an Insurable Risk

1. Large numbers of exposure units

2. Definite and measurable loss

3. The loss must be fortuitous

4. The loss must not be catastrophic

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Other Facets of Insurable Risk

1. Randomness-adverse selection

2. Economic feasibility

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Self-Insurance

1. Definitional impossibility

2. Acceptable operational definition• enough exposures for predictability• financially dependable• geographic dispersion