Law of Large Numbers
The law of large numbers states that the average claims cost of an insurance portfolio converges toward the theoretical expected value as portfolio size grows.
Concept
The law of large numbers is a fundamental theorem of probability theory stating that the arithmetic mean of a large number of independent, identically distributed random variables converges toward the theoretical expected value of that distribution as the number of observations grows.
Relevance as a Founding Principle of Insurance
The law of large numbers forms the fundamental mathematical principle underlying the idea of insurance as risk pooling within a collective: the larger and more homogeneous an insurance portfolio, the more closely the actually observed average claims cost approaches the theoretically expected value, thereby making risks calculable and providing the basis for risk-adequate premium setting.
Limitations of the Law of Large Numbers
The law of large numbers assumes that the individual risks within a portfolio are largely independent of one another; for strongly correlated or accumulation-prone risks, such as natural catastrophes or pandemics, the risk-pooling effect applies only to a limited extent, since many individual risks can occur simultaneously, making special measures such as reinsurance or alternative risk transfer instruments necessary.