Karl H. Borch

Karl H. Borch

Developments in insurance economics in particular and the economics of uncertainty in general over the past few decades provide a vivid illustration of the interplay between abstract theorizing and applied research. In any account of these developments, the specific early contributions of Karl Henrik Borch, from the late fifties on, are bound to stand out.

During his period as a professor, from 1963 till his death in 1986, he had more than 150 publications in scientific journals, proceedings and transactions from scientific conferences, among them three books. Borch took part in the activities of a number of professional organizations with enthusiasm and presented his ideas in innumerable lectures, discussions and written contributions.

He became a driving force behind the maturation, extension, and the credibility of the Geneva Association group of risk and insurance economists. In 1990 this association honored his memory by publishing the volume Risk, Information and Insurance: Essays in the Memory of Karl H. Borch.


Karl H. Borch was born in 1919. During the Second World War he fled to London, where at first he was attached to the Norwegian exile government, and later he spent three years with the Free Norwegian Forces in Great Britain. When he returned to Norway after the war, he graduated with a master of science in actuarial mathematics in 1947. He was employed in the insurance industry for brief periods both before the war and after his graduation. From 1947 through 1959 he worked for international organizations, such as UNESCO, UNICEF, and OECD.

The only early indication of a future scientific career may be the spring semester of 1953, which he spent as a research associate at the Cowles Commission for Research in Economics at the University of Chicago. Here he met some of the world’s leading economists and as a result of this short stay he published an article in Econometrica (1953) about the effects on demand for consumer goods from changes in the distribution of income.

Stepping into academia

The opportunity came in 1959 at the Norwegian School of Economics and Business Administration (NHH) through a donation of a chair in insurance. First Borch was given the scholarship associated with the chair, used this three year period to take his doctorate at the University of Oslo in 1962, and was finally appointed professor of insurance at the NHH in 1963. This step in 1959 must have been perceived as a rather risky one, both for him and for NHH.  Borch was then 40 years of age, his academic credentials were limited, and even being an actuary with some - although rather limited - experience, he had not written anything within the field. But Borch fearlessly accepted the new challenge.

In Who’s Who in Economics (2nd Ed. 1986, 3rd Ed. 1999) he wrote: “When in 1959 I got a research post which gave me almost complete freedom, as long as my work was relevant to insurance, I naturally set out to develop an economic theory of insurance”. This may sound simple and uncomplicated. That he within a year should have made a decisive step in that direction is amazing. What he did during these first years of his “real” research career was to write the first of a long series of seminal papers, which were to put him on the map as one of the world’s leading scholars in his field.

The nature of the step is also noteworthy. Borch was familiar with recent theoretical papers leading up to the subsequent reformulation of general equilibrium theory by Arrow and Debreu in Econometrica (1954). He was well aware of the von Neumann and Morgenstern expected utility representation of preferences, and was also influenced by the subjective expected utility representation proposed by Savage.

He understood perfectly the significance of such works as well as their limitations, at a time when very few economists had taken notice. As he explained more explicitly in 1962, he attributed that lack of recognition to the fact that these “relatively simple models appear too remote from any really interesting practical economic situation... However, the model they consider gives a fairly accurate description of a reinsurance market.”

One important contribution in the early papers by Karl Borch in Skandinavisk Aktuarietidskrift (1960) and Econometrica (1962) was to derive testable implications from the abstract model of general equilibrium with markets for contingent claims. In this way, he brought economic theory to bear on insurance problems, thereby opening up that field considerably. He also brought the experience of reinsurance contracts to bear on the interpretation of economic theory, thereby enlivening considerably the interest for that theory.

In Borch’s model the market is complete by construction, assuming that any reinsurance contract can be signed, so he did not need the rather theoretical, and artificial, market consisting of so-called Arrow-Debreu securities. This fact made his model very neat, indeed, and opened up for many important insights.

The economics of uncertainty

Borch did not write only about insurance, but it is fair to say that after he started his academic career, practically his entire production was centered on the topic of uncertainty in economics in one form or the other. Many of his thoughts around the economics of uncertainty were formulated in his successful book The Economics of Uncertainty, published in 1968 by Princeton University Press (also available in Spanish, German, and Japanese). It illustrates the close connection between economics of uncertainty and insurance economics, at least as seen from Karl Borch´s point of view.

Borch helped establish, and travelled repeatedly, the bridge that links the theory of reinsurance markets and the “Capital Asset Pricing Model” (CAPM), developed by his former student Jan Mossin, among others. Although Borch was keenly conscious of the restrictive nature of the assumptions underlying the CAPM, he often used that model as an illustration, stressing that “the applications of CAPM have led to deeper insight into the functioning of financial markets”. He also published an influential and clarifying criticism on the limitations on mean-variance analysis, in “A Note on Uncertainty and Indifference Curves” in Review of Economic Studies (1969).

It may be of some interest to relate Borch’s view of the economics of uncertainty to the theory of “contingent claims” in financial economics, the interest of which has almost exploded, following the seminal 1973 option prizing paper by Black and Scholes.  In order to really understand the economic significance of these developments, it is well worth to study the theory in Borch´s language (as in his 1968 book), where many of the concepts are more transparent than in the “modern” counterpart.

For example, Karl Borch made important, early contributions towards the understanding of the notion of complete markets. The famous linear pricing rule preventing arbitrage is the neoclassical one just as in Borch’s world, where the main problem is to characterize the “state price deflator” from underlying economic primitives.

Insurance economics

Borch’s pioneering work on Pareto-optimal risk exchanges in reinsurance opened a new area of actuarial science, which has been in continuous growth since. This research field offers a deeper understanding of the preferences and behavior of the parties in an insurance market. The theory raises and answers questions that could not even be put into shape by traditional actuarial handicraft: how can risk be optimally shared between economic agents, and how should the insurance industry best be organized in order to further social security and public welfare? 

Finally, it should be mentioned that Borch gave many contributions to the application of game theory in insurance. With his clear intellect Borch was typically attracted to game theory. In particular he characterized the Nash bargaining solution in a reinsurance syndicate. He also analyzed the moral hazard problem in insurance by a Nash equilibrium in mixed strategies, among many other applications.

Some of his articles have been collected in his 1974 book The Mathematical Theory of Insurance, published by Lexington Books (and with a foreword by Kenneth J. Arrow). Karl Borch often related advanced theoretical results to casual observations - sometimes in a genuinely entertaining manner, which transmits to younger generations a glimpse of his wit and personal charm.

Several of his papers follow a simple lucid pattern: after a brief problem-oriented introduction, the first-order conditions for efficient risk-sharing are recalled, then applied to the problem at hand; the paper ends with a discussion of applicability and confrontation with stylized facts. The author prefers a succession of light touches, in numbered subsections, to formal theorems and lengthy discussions.

At his death he was working on a manuscript to a fundamental textbook in the economics of insurance. Supplemented by some of Borch’s papers, and with the help of professors Agnar Sandmo and Knut K. Aase, this manuscript was in 1990 published as Economics of Insurance by North Holland. This book was translated into Chinese in 1999.

Karl Borch’s importance to NHH

His appointment to professor coincided with the beginning of the big expansion period in the 1960s, which transformed the School from a small to a relatively large institution of its type. For the generation of researchers who got attached to NHH as research assistants in this period, Borch had an enormous influence – as teacher, advisor, and as a role model. He gave the first lectures at graduate level, and was personally advisor for a long series of master’s (licentiate) and doctoral candidates.

As advisor he stimulated his students to study abroad, and using his broad network of international contacts he helped them to get to the best places. He also encouraged them to raise their ambitions and write with a view towards international publishing. The international recognition NHH enjoys today is based on the fundamental efforts by Borch in this period. We still enjoy the fruits from his efforts.

Naturally enough Borch influenced the research orientation of a group of younger scholars - over a period NHH was in fact known as the place where “everybody” was concerned with uncertainty. Both for his own research and for his inspiration and encouragement to the research environment, he was the obvious choice to receive the NHH Price for Excellent Research, awarded for the first time at the School’s fiftieth anniversary in 1986. Borch remained as the professor of insurance at NHH, until his untimely death on December 2, 1986, just barely before retirement at pensionable age.

Karl Borch will be remembered by colleagues and students at the NHH and in many other places as a guide and source of inspiration, and by a large number of people all over the world as a gentle and considerate friend who had concern for their work and everyday life.

In 2002 the Department of Finance and Management Science at NHH established an annual "Karl Borch Lecture" series, in honor of Borch. The lecture is on a current research topic and given by distinguished scholars, whose research capture the pioneering spirit  of Karl Borch, but not necessarily his fields of research in a narrow sense.


Adapted from: Aase, K. K. (2003) “The life and career of Karl H. Borch”, Discussion Paper, 2003/5, Department of Finance and Management Science, NHH. Later published in J. L. Teugels and B. Sundt (Eds.) Encyclopedia of Actuarial Science, Vol 1, 2004, pp 191-195, Wiley.

Karl H. Borch

Karl H. Borch was a professor at NHH between 1963 and 1986, and is considered one of the founders of economics of uncertainty, counting 150 scientific articles in journals and conference proceedings, and three books.


Selected Works by Karl H. Borch

Authors Title Publication

Borch, Karl H.

Effects on Demand of Changes in the Distribution of Income

Econometrica, 1953, 21(2), 325-331

Borch, Karl H.

The Safety Loading of Reinsurance Premiums

Skandinavisk Aktuarietidsskrift, 1960(3-4), 163-184

Borch, Karl H.

Reciprocal Reinsurance Treaties

ASTIN Bulletin, 1960, 1(4), 170-191

Borch, Karl H.

Reciprocal Reinsurance Treaties seen as a Two-Person Cooperative Game

Skandinavisk Aktuarietidsskrift, 1960(1-2), 29-58

Borch, Karl H.

Equilibrium in a Reinsurance Market

Econometrica, 1962, 30(3), 424-444

Borch, Karl H.

The Theory of Risk

Journal of the Royal Statistical Society. Series B (Methodological), 1967, 29(3), 432-467

Borch, Karl H.

The Economics of Uncertainty

Princeton University Press1968

Borch, Karl H.

General Equilibrium in the Economics of Uncertainty

Risk and Uncertainty: Proceedings of a Conference held by the International Economic Association (Eds.: Karl H. Borch and Jan Mossin), 1968, Macmillan

Borch, Karl H.

A Note on Uncertainty and Indifference Curves

Review of Economic Studies, 1969, 36(1), 1-4

Borch, Karl H.

The Mathematical Theory of Insurance

D. C. Health / Lexington Books, 1974

Borch, Karl H.

The Monster in Loch Ness

Journal of Risk and Insurance, 1976, 43(3), 521-525

Borch, Karl H.

The Price of Moral Hazard

Scandinavian Actuarial Journal, 1980(3), 173-176

Borch, Karl H.

Additive Insurance Premiums

Journal of Finance, 1982, 37(5), 1295-1298

Borch, Karl H.

Insurance Premiums in Competitive Markets

Geld, Banken und Versicherungen, 1982, Band II (Eds.: Göppl and Henn), 1983, 827-841, Verlag Versicherungswirtschaft Karlruhe

Borch, Karl H.

Static Equilibrium under Uncertainty and Incomplete Markets

Geneva Papers on Risk and Insurance, 1983, 8(4), 307-315

Borch, Karl H.

A Theory of Insurance Premiums

Geneva Papers on Risk and Insurance, 1985, 10(3), 192-208

Borch, Karl H.

Economics of Insurance

Advanced Textbooks in Economics, 1990, 29 (Eds.: Knut K. Aase and Agnar Sandmo), North Holland