Bernstein, Peter L. Against the Gods:  The Remarkable Story of Risk.  John Wiley and Sons:  New York, 1996.

A history of risk taking and a cautionary tale about the instruments used to control risk, Bernstein's work has a uroborean thesis:  the success of capitalism rests on the modern, popular and correct conviction that risks can be controlled, and by contrast, the past is a not a guide to the future and people do not and have never behaved rationally in responding to risk.

Bernstein's work begins with the Greeks, and like other historians, asks why the Greeks, who loved games, betting, and mathematics, didn't proceed farther  -- in this case, farther along the path of mathematical quantification of risk.  Following Shmuel Sambursky, Bernstein posits that the Greeks preferred chasing the ideal -- the proofs of geometry, the golden mean spiral of a Fibonacci sequence --  to following the fuzzy problems that comprise defining uncertainty.  Businessmen of all ages -- from Greeks to the present day -- used financial instruments to control risk (304), but the theory of uncertainty developed slowly, building from the work of Renaissance mathematicians.

Groundwork for the theory of risk began with numbers themselves.  Until the Arabic numeral system spread along with Islam after 600 AD, it was simply impossible to do certain kinds of equations easily. (Bernstein makes this point cheaply by using Roman numerals for the pages of that chapter.) Crucial to new thinking was the zero, which at once allowed for only ten symbols to represent all the digits possible, and also for a visual and logical progress in numbers (1, 10, 100, 1000).  Fibonacci's Liber Abaci, written in 1202 on the Arabic numbering system, received the endorsement of the Holy Roman Emperor, Frederick II, but the system gained most rapidly after the invention of moveable type, when it became obvious that it would be difficult to falsify a printed (rather than a handwritten) number.

In his 1494 Summa de Arithmetic the monk Luca Paccioli posed a question about the stakes to be divided from an unfinished game of balla.  Berstein pinpoints that puzzle as "the threshold of the quantification of risk." (43, italics his). Dicing and debating, combing the heavens, comparing peapods, praying and gathering statistics: in Bernstein's dizzying (but competent) collation of a diversity of thinkers and fields, Girolama Cardano, physician, gamester, author of Ars Magna is followed by Pascal's wager and triangle, the dour Bernoulli family, John Graunt, notions salesman and fanatic statistician, Lloyds of London, Edmund Halley of later comet fame, and Gauss's quincunx.  The key historical points of risk management may be summarized as follows:
Mathematical models for variations and outcomes were solved relatively early.  "By the end of the seventeenth century, about a hundred years after the death of Cardano and less than fifty years after the death of Galileo, the major problems in probability analysis had been solved."  (56) Pascal and Fermat offered crucial assistance to the next step by solving the just division of the balla games' stakes.  But more importantly, they anticipated Bernoulli, by understanding that risk is valued differently by different people.  This concept is also known as utility, or the strength of our desire for something (71). In non-academic discourse, utility early urged the development of ship lists and information exchanges such as Lloyds of London. (Bernstein notes traders have been employing dissymmetrical information as a hedge against risk for a long time.) Governments, like traders, took a practical interest in information, specifically in information that would help to estimate the amount of revenue that could be extracted to fund wars or peacetime projects.  Statisticians like Graunt and Halley, who worked on life expectancy table offered a powerful tool for to pricing the revenue on annuities.   Returning to a review of more academic developments, Bernstein reviews the eighteenth and nineteenth century.  He covers the  development of Bernoulli's Law of Large numbers, the Benthamites, Gauss's Bell Curve and the concept of the regression to the mean.  Like Fibonacci's spiral, properly arranged, lovely patterns emerge from a mass of confusing data. The problem is -- and this is the point of Bernstein's story -- that all of these mathematical tools are crucial for conveying a sense that Nature (capital N) repeats herself predictably.  Capitalists need to believe that risk is manageable to start accumulating and then risking that capital.  However, for there to be a risk to take, an unknown gain to be made, an imperfection in repetition is crucial.

The twentieth century breaks significantly with the mathematics of Nature and with the Renaissance and Enlightenment view that man will act rationally.  Kenneth Arrow and John Maynard Keynes articulate for Bernstein the question at the heart of risk management:  how to predict human irrationality?   Bernstein suggests that some of these answers may be found in psychology, in the work of Kahneman and Tversky (an exciting chapter, 16!) demonstrating the strongly patterned loss-aversion responses of their subjects.  He also suggests that derivatives, embodying as they do uncertainty -- "the product in derivative transactions is uncertainty itself." (314)  -- allows for a finely-tuned spreading of risk for almost any business situation.  Finally, Bernstein returns to his thesis: Nature has to be uncertain, and we have to believe that we are able to control it partially, for wealth to grow, but always, only, we live in the twilight of probability (337).

Points to pursue?
Double entry bookkeeping, p. 42
Cultural (Greek) aversion to risk. p. 17
Kahneman and Tversky, Chap. 16  historical patterns to risk/loss avoidance.