Lecture 4: Risk Sharing

Insurance

"Insurance is the pooling of fortuitous losses by transfer of such risks to insurers, who agree to indemnify for such losses, to provide other pecuniary benefits on their occurrence, or to render services connected with the risk."

Law of Large Numbers

If the number of risks in the portfolio tends to infinity, the probability that the average outcome differs from expected value is positive tends to zero.

Basic Characteristics of Insurance

Payment of fortuitous losses risk transfer indemnification pooling of risks

Pooling of Risks

enables the policyholder to replace uncertain payments with a certain payment

The Central limit theorem

under the same assumption as the Law of Large Numbers, the average outcome approaches a Normal distribution with mean µ and standard deviation as σ / n n gets very large.