**"Against the gods" **is a beautiful narrative on the history of risk management. Peter L Bernstein , the author of the book has a done a terrific work of narrating the evolution of risk measurement. The book is divided in to 5 periods where the story of risk is presented.

**The five demarcated periods are Uptil 1200 ,1200-1700,1700-1900,1900-1960,Post 1960.**

In each of these periods, the author talks about various personalities involved. Let me recap the book in the same manner, listing the main items from each of these time periods.

Firstly, something about the title of the book " against the gods" . It is so named because the author brings out a pattern in his narrative i.e, through the history of the development of risk, there was one powerful idea that galvanized the development of risk, the idea that humans are in control of their destiny Vs Gods who control the destiny.

**Pre-1200**

**Numbers Era**

Pre-1200's was a period which was characterized by folks trying to understand and formulate numbers.

**Liber Aabaci**which was the first treatment on the theory and application of various aspects of numbers. This was also a period when the development of 0 made a significant impact in the way numbers were used

**Period 1200 – 1700 Outstanding facts Era**

**summa**, he gave tables for 60*60 multiplication operations. He was a numbers man and he posed the most famous problem of all times, the problem of balla.

*A and B are playing a fair game of balla. They agree to continue until one has won 6 rounds. The game actually stops when A has won 5 and B has won three. How should the stakes be divided***Ars Magna**( The great art) which was followed by Liber de Ludo Algae( Book on games of chance). This appears to have been the first serious effort to develop statistical principles of probability. Probability always had 2 meanings one looking in to the future, the other interpreting the past, he former cncerned with our opinions and the latter concerned with what we actually know. However the idea of measuring probability came later which means " How much can we accept of what we know ? . In a sense the book

**Liber de Ludo Algae**was a primer to risk management. Cardano is credit for an bringing a new terminology like fair dice, circuit, combinations,odds ratio etc. Interestingly , the word "fair dice" came in to being because he had spent years on the gambling table and he could see how various players cheated. However his book was not accessible for a lot of mathematicians in the renaissance time for various reasons

**French Connection :**

Pascal Chevalier Fermat

These two mathematicians were great in their respective fields but it was Chevalier De mere , a noble man, a person with keen interest in gambling and mathematics , posed the **old problem of balla**. In a series of communications between Pascal and Fermat, Pascal came up with a triangle , popularly referred to as Pascal's triangle to calculate the odds for solving problem of balla. This was the first time a mathematical tool was used to forecast, in this case, the prize money in the game. **Pascal's triangle** was a neat way to summarize the events that could happen in a probabilistic sense. For example if there are 5 games are to be played between 2 folks, then the 2 power 5 = 32 corresponds to the 5th row in the triangle from which one can read different types of events that happen.

**Remarkable Notions Man:**

John Graunt , a merchant and William Petty were folks who used statistical inference techniques. Graunt was a man who was obsessed with verifying common every day notions. With the help of Petty, he developed a method of drawing inferences from a small sample .Both were extremely interested in the organization of human society rather than the science of nature However they never used the word probability . Estimating the odds of uncertain events had to wait until 1700-1900 , a period appropriately titled "Measurement Unlimited"

**Period 1700 – 1900**

**Measurement Unlimited Era**

**Meet the Bernoulli family:**

Daniel Bernoulli is credited to have brought in the element of risk taker in to the whole game of risk. He hypothesized that the importance of wealth for an individual is inversely proportional to the amount of wealth accumulated. From the world of simple dice, roulette wheels, the inclusion of the player brought in a whole new dimension to the risk management development. **Utility as a concept had a tremendous influence on the way risk management principles** were developed in the later years.Petersburg paradox is a classic example of utility concept explained by Bernoulli,

**Law of Large numbers**which says that :

*Average of large number of throws will be more likely than the average of a small number of throws to differ from the true average by less than some stated amount..*

**normal curve distribution**.The third person who belonged to the same era and contributed to the formulation of a posterior probabilities is Bayes. Though none of his work got published when he was alive, his work had a great influence later. Possibly, the most important contribution of bayes was the precise problem formulation :

*Given the number of times in which an unknown event has happened and failed, Required , the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named ?*

**central limit theorem deals with the average of averages.**

In simple words, this theorem says, if you pick a large sample, take its average, do it multiple times, and plot the averages of all the sample, the frequency distribution is a normal distribution..This is an amazing pattern because the actual distribution of random variables can be anything, but sample averages tend to be normal.

**"Regression to mean"**. In the long term, the high and low values of a variable stabilize to an average value. He also hypothesized that influences on a variable themselves had to be normally distributed for the dependent variable to be normally distributed. This is nothing but the popular theorem that sum of N normal random variables is another normal random variable.

**Period 1900 – 1960**

**Clouds of Vagueness and the demand for Precision**

The essence of risk management lies in maximizing the areas where we have some control over the outcome while minimizing the areas where we have absolutely no control over the outcome and the linkage between effect and cause is hidden from us.Two people from this era wanted to attribute causality to the every day events. One was Laplace and other was Henri Poincare. However both agreed to the fact that not always, there is complete information to attribute the causality.

Hence the development of** reject or non-reject hypothesis **came in to being . It was thought one can never be certain about any thing. only one can reject or not reject a hypothesis with some confidence level. Thus statistical inference and hypothesis testing concepts flourished .

**Post 1960**

**Degrees of Disbelief & Exploring uncertainty**

The last part of book focuses on prospect theory, derivatives such as futures and options to tame uncertainty.

I have tried to give a pretty elaborate summary of the book. However there are a lot of aspects which you can cherish if you go through the details behind the chronology of events. .

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