1、 rigorous. So, it was in the 1600s that probability theory started to get written down as a theory and many things then happened in that century that, I think, are precursors both to finance and insurance. One was in the 1600s when people started constructing life tables. What is a life table? Its a
2、 table showing the probability of dying at each age, for each age and sex. Thats what you need to know if youre going to do life insurance. So, they started to do collecting of data on mortality and they developed something called actuarial science, which is estimating the probability of people livi
3、ng. That then became the basis for insurance. Actually, insurance goes back to ancient Rome in some form. In ancient Rome they had something called burial insurance. You could buy a policy that protected you against your family not having the money to bury you if you died. In ancient culture people
4、worried a great deal about being properly buried, so thats an interesting concept. They were selling that in ancient Rome; but you might think, but why just for burial? Why dont you make it into full-blown life insurance? You kind of wonder why they didnt. I think maybe its because they didnt have t
5、he concepts down. In Renaissance Italy they started writing insurance policies-I read one of the insurance policies, its in the Journal of Risk and Insurance-and they translate a Renaissance insurance policy and its very hard to understand what this policy was saying. I guess they didnt have our lan
6、guage, they didnt-they were intuitively halfway there but they couldnt express it, so I think the industry didnt get really started. I think it was the invention of probability theory that really started it and thats why I think theory is very important in finance. Some people date fire insurance wi
7、th the fire of London in 1666. The whole city burned down, practically, in a terrible fire and fire insurance started to proliferate right after that in London. But you know, you kind of wonder if thats a good example for fire insurance because if the whole city burns down, then insurance companies
8、would go bankrupt anyway, right? London insurance companies would because the whole concept of insurance is pooling of independent probabilities. Nonetheless, that was the beginning. The Universal Principle of Risk Management: Pooling and the Hedging of Risks4Were also going to recognize, however, t
9、hat insurance got a slow start because-I believe it is because-people could not understand the concept of probability. They didnt have the concept firmly in mind. There are lots of aspects to it. In order to understand probability, you have to take things as coming from a random event and people don
10、t clearly have that in their mind from an intuitive standpoint. They have maybe a sense that I can influence events by willing or wishing and if I think that-if I have kind of a mystical side to me, then probabilities dont have a clear meaning. It has been shown that even today people seem to think
11、that. They dont really take, at an intuitive level, probabilities as objective. For example, if you ask people how much they would be willing to bet on a coin toss, they will typically bet more if they can toss the coin or they will bet more if the coin hasnt been tossed yet. It could have been alre
12、ady tossed and concealed. Why would that be? It might be that theres just some intuitive sense that I can-I dont know-I have some magical forces in me and I can change things. The idea of probability theory is that no, you cant change things, there are all these objective laws of probability out the
13、re that guide everything. Most languages around the world have a different word for luck and risk-or luck and fortune. Luck seems to mean something about you: like Im a lucky person. I dont know what that means-like God or the gods favor me and so Im lucky or this is my lucky day. Probability theory
14、 is really a movement away from that. We then have a mathematically rigorous discipline. Now, Im going to go through some of the terms of probability and-this will be review for many of you, but it will be something that were going to use in the-So Ill use the symbol P or I can sometimes write it ou
15、t as prob to represent a probability. It is always a number that lies between zero and one, or between 0% and 100%. “Percent“ means divided by 100 in Latin, so 100% is one. If the probability is zero that means the event cant happen. If the probability is one, it means that its certain to happen. If
16、 the probability is-Can everyone see this from over there? I can probably move this or cant I? Yes, I can. Now, can you now-youre the most disadvantaged person and you can see it, right? So thats the basic idea. One of the first principles of probability is the idea of independence. The idea is that
17、 probability measures the likelihood of some outcome. Lets say the outcome of an experiment, like tossing a coin. You might say the probability that you toss a coin and it comes up heads is a half, because its equally likely to be heads and tails. Independent experiments are experiments that occur w
18、ithout relation to each other. If you toss a coin twice and the first experiment doesnt influence the second, we say theyre independent and theres no relation between the two. One of the first principles of probability theory is called the multiplication rule. That says that if you have independent
19、probabilities, then the probability of two events is equal to the product of their probabilities. So, the Prob(A and B) = Prob(A)*Prob(B). That wouldnt hold if theyre not independent. The theory of insurance is that ideally an insurance company wants to insure independent events. Ideally, life insur
20、ance is insuring people-or fire insurance is insuring people-against independent events; so its not the fire of London. Its the problem that sometimes people knock over an oil lamp in their home and they burn their own house down. Its not going to burn any other houses down since its just completely
21、 independent of anything else. So, the probability The Universal Principle of Risk Management: Pooling and the Hedging of Risks5that the whole city burns down is infinitesimally small, right? This will generalize to probability of A and B and C equals the probability of A times the probability of B
22、times the probability of C and so on. If the probability is 1 in 1,000 that a house burns down and there are 1,000 houses, then the probability that they all burn down is 1/1000 to the 1000th power, which is virtually zero. So insurance companies thenBasically, if they write a lot of policies, then
23、they have virtually no risk. That is the fundamental idea that may seem simple and obvious to you, but it certainly wasnt back when the idea first came up. Incidentally, we have a problem set, which I want you to start today and it will be due not in a week this time, because we have Martin Luther King Day coming up, but it will be due the Monday following that. If you follow through from the independent theory, theres one of the basic relati
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