In parallel to his business career, Lundberg worked on a theory of collective risk. In 1903, he finished his doctoral thesis,
Approximations of the Probability Function/Reinsurance of Collective Risks. This introduced the compound
Poisson process and involved work on the
central limit theorem. Cramér writes that the thesis has a reputation for being impossible to understand but, that looked at now, "one cannot help being struck by his ability to deal intuitively with concepts and methods that would have to wait another thirty years before being put on a rigorous foundation." Cramér mentions later work by
Andrey Kolmogorov and
William Feller but it was Cramér himself who developed Lundberg's ideas on risk and linked them to the emerging theory of
stochastic processes. Focardi & Fabozzi describes Lundberg's thesis as a milestone in actuarial mathematics. It was the first to define a collective theory of risk and to apply a sophisticated probabilistic formulation to the insurance ruin problem. Lundberg’s work anticipated many future developments of
probability theory, including what was later to be known as the theory of point processes. Lundberg's theory, together with that of French mathematician
Louis Bachelier, was ahead of its time and inspired the subsequent development of probability theory. But the type of mathematics implied by his work could not be employed completely until the development of digital
computers. Because he published many of his major works in
Swedish, Lundberg's work went unnoticed by the actuarial community for nearly 30 years. However, eventually Lundberg's ideas became known largely through the work of Cramér and his students. Although Lundberg published some work in
German, the international scientific language of the time, Lundberg's thesis and most of his subsequent writings were in Swedish. His mathematical language did not travel easily, either. == Discussions ==