Leo Levenius: The Cramér–Lundberg Ruin Theory

Abstract:

Ruin theory is a branch of insurance mathematics that studies the event of an insurance company not having sufficient capital to pay its commitments to its customers, ruin. The insurance company receives a deterministic stream of premiums, while the claim costs follow a stochastic process. We want to model the distribution of the capital over time in order to determine the premium needed to keep the probability of ruin sufficiently small. This talk centers around the foundational contributions to the field made by Swedish mathematicians Filip Lundberg and Harald Cramér in the early 20th century, as well as some of my own results. I aim to be understandable to most mathematicians; just some basic knowledge of probability theory could be useful. The talk is based on a chapter from my master's thesis, Den Cramérska assuransmatematiken (2025).