# The Insurance Device

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

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