On a law of large numbers for insurance risks

TL;DR

This paper establishes a strong law of large numbers for insurance risks stemming from a single catastrophic event, emphasizing diversification effects through optimal risk allocation to multiple reinsurers or investors.

Contribution

It introduces a law of large numbers applicable to catastrophic insurance risks, highlighting the role of diversification and optimal risk distribution.

Findings

Demonstrates a strong law of large numbers for catastrophic risks.

Shows diversification reduces variability in aggregate risk.

Highlights optimal risk allocation as a key factor.

Abstract

This note presents a kind of the strong law of large numbers for an insurance risk caused by a single catastrophic event rather than by an accumulation of independent and identically distributed risks. We derive this result by a large diversification effect resulting from optimal allocation of the risk to many reinsurers or investors.