The Insurance Device

Chapter 3

Private and Social

• Private (Commercial)– Auto, Life etc.

• Social (Publicly provided)– Social security, Medicare etc

• Quasi-social– FDIC, SIPC, PBGC etc.

What is insurance?

• The insured exchanges a large uncertain loss for a small certain cost

• The insured can be an individual or a corporation

What is involved in insurance?

• Risk gets transferred from individual to a group

• A group of individuals can agree to share the losses of any one member (mutual insurance)

• There is risk reduction through pooling or diversification (The law of large numbers)

Two uses of the law of large numbers

• Estimation of loss probability becomes accurate with large data sets

• Selling insurance becomes feasible when risk is pooled (diversified)

Some probability concepts

• Subjective and objective

• A priori and a posteriori

• Uncorrelated outcomes and variance of sums

Pooling and risk reduction

• Let x represent the loss from a set of policies

• Let there be many such identical sets that are uncorrelated with each other

• As a compnay adds additional sets to its portfolio, the variance increases linearly

• Standard deviation increases as the square root of n

Pooling and risk reduction

• The standard deviation per set declines (risk reduction)

• The standard deviation of losses for the portfolio increases

• Reinsurance allows the insurer take a small piece of a large pie

• Need pooling and sharing for risk reduction

Some problems

• Stability of the probability process

• Adverse selection (unobservable knowledge)

• Morale hazard (unobservable action)

• Economic feasibility

Self insurance

• Large firms may have a large number of homogenous exposure units

• May be able to do in-house pooling

• Risk divided up among shareholders

• May have to be funded adequately for legal/regulatory reasons