The Insurance Device

1. The Insurance Device Chapter 3

2. Private and Social • Private (Commercial) • Auto, Life etc. • Social (Publicly provided) • Social security, Medicare etc • Quasi-social • FDIC, SIPC, PBGC etc.

3. What is insurance? • The insured exchanges a large uncertain loss for a small certain cost • The insured can be an individual or a corporation

4. 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)

5. 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)

6. Some probability concepts • Subjective and objective • A priori and a posteriori • Uncorrelated outcomes and variance of sums

7. 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

8. 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

9. Some problems • Stability of the probability process • Adverse selection (unobservable knowledge) • Morale hazard (unobservable action) • Economic feasibility

10. 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