Filip Lundberg
Encyclopedia
Ernst Filip Oskar Lundberg (31 December 1876 - 2 June 1965) Swedish actuary
, founder of mathematical risk theory
and managing director of several insurance companies.
According to Harald Cramér
, "Filip Lundberg's works on risk theory were all written at a time when no general theory of stochastic processes existed, and when collective reinsurance
methods, in the present sense of the word, were entirely unknown to insurance companies. In both respects his ideas were far ahead of their time, and his works deserve to be generally recognized as pioneering works of fundamental importance."
Filip Lundberg's father, Philip Lundberg, was a school teacher and Filip's first ambition was to follow his father's career. He studied mathematics
at the University of Uppsala, graduating in 1896 and receiving his Licentiate
in 1898. But, instead of becoming a teacher, Filip joined a newly founded insurance company. He soon moved to a second company where he was appointed actuary
and at the age of 28 became its managing director. He went on to become a leader of the industry, managing other companies, serving as chairman of the Association of Swedish Life Insurance Companies for ten years and sitting on government committees on insurance.
In parallel to his business career Lundberg worked on a theory of collective risk theory. 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.
Lundberg's ideas became known largely through the work of Cramér and his students. Although he 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.
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
, founder of mathematical risk theory
Risk theory
Risk theory connotes the study usually by actuaries and insurers of the financial impact on a carrier of a portfolio of insurance policies. For example, if the carrier has 100 policies that insures against a total loss of $1000, and if each policy's chance of loss is independent and has a...
and managing director of several insurance companies.
According to Harald Cramér
Harald Cramér
Harald Cramér was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. He was once described by John Kingman as "one of the giants of statistical theory".-Early life:Harald Cramér was born in Stockholm, Sweden on September...
, "Filip Lundberg's works on risk theory were all written at a time when no general theory of stochastic processes existed, and when collective reinsurance
Reinsurance
Reinsurance is insurance that is purchased by an insurance company from another insurance company as a means of risk management...
methods, in the present sense of the word, were entirely unknown to insurance companies. In both respects his ideas were far ahead of their time, and his works deserve to be generally recognized as pioneering works of fundamental importance."
Filip Lundberg's father, Philip Lundberg, was a school teacher and Filip's first ambition was to follow his father's career. He studied mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
at the University of Uppsala, graduating in 1896 and receiving his Licentiate
Licentiate
Licentiate is the title of a person who holds an academic degree called a licence. The term may derive from the Latin licentia docendi, meaning permission to teach. The term may also derive from the Latin licentia ad practicandum, which signified someone who held a certificate of competence to...
in 1898. But, instead of becoming a teacher, Filip joined a newly founded insurance company. He soon moved to a second company where he was appointed actuary
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
and at the age of 28 became its managing director. He went on to become a leader of the industry, managing other companies, serving as chairman of the Association of Swedish Life Insurance Companies for ten years and sitting on government committees on insurance.
In parallel to his business career Lundberg worked on a theory of collective risk theory. In 1903 he finished his doctoral thesis, Approximations of the Probability Function/Reinsurance of Collective Risks. This introduced the compound Poisson process
Poisson process
A Poisson process, named after the French mathematician Siméon-Denis Poisson , is a stochastic process in which events occur continuously and independently of one another...
and involved work on the central limit theorem
Central limit theorem
In probability theory, the central limit theorem states conditions under which the mean of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed. The central limit theorem has a number of variants. In its common...
. 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
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.-Early life:Kolmogorov was born at Tambov...
and William Feller
William Feller
William Feller born Vilibald Srećko Feller , was a Croatian-American mathematician specializing in probability theory.-Early life and education:...
but it was Cramér himself who developed Lundberg's ideas on risk and linked them to the emerging theory of stochastic processes.
Lundberg's ideas became known largely through the work of Cramér and his students. Although he published some work in German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
, 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
- Harald CramérHarald CramérHarald Cramér was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. He was once described by John Kingman as "one of the giants of statistical theory".-Early life:Harald Cramér was born in Stockholm, Sweden on September...
(1969) Historical Review of Filip Lundberg's Work on Risk Theory, Skandinavisk Aktuarietidskrift (Suppl.), 52, 6-12. Reprinted in The Collected Works of Harald Cramér edited by Anders Martin-Löf, 2 volumes Springer 1994.
- K. Englund and A. Martin-Löf (2001) Ernst Filip Oskar Lundberg, Statisticians of the Centuries (ed. C. C. Heyde and E. Seneta) pp. 308-311. New York: Springer.
External links
- There is a photograph at Lundberg, Ernst Filip Oskar on the Portraits of Statisticians page.
