# How much do you pay for your insurance?

Have you ever heard about Game Theory? Do you know anything about how people make decisions? Should you know, you’ll likely understand a bit how insurance companies price their products. Let me introduce you briefly how it works (the following explanation is highly simplified but to begin with, easy to understand).

Firstly, assume you have an initial wealth “W” and if you have any sort of accident, you’ll lose “L” (with a probability equal to “p“).  How much are you willing to pay (“P”) to insure against this possible loss? In other words, which P (price) makes no difference between taking out insurance and not taking it out?

We can form here a simple decision tree:

On the other hand, we take out insurance policies because we don’t like certain types of risks. But not everyone has the same attitude towards risk. People can be classified into:

• Risk averse
• Risk neutral
• Risk lover

Assume now that our attitude towards risks can be presented by the function U(x) (utility function). Assume as well that insurance companies have enough information to classify each of us in one of the above mentioned types, which translates into knowing – approximately – our utility function U(x).

Coming back to the decision tree, without insurance, we’ll get an expected utility equal to:

EU = p*U(W-L) + (1-p)*U(W)

Therefore, the maximum price satisfies:

U(W-P) = p*U(W – L) + (1-p)*U(W)

Knowing the utility function, an approximation of the individual’s wealth and the probability of an accident, it’s easy to get the maximum price someone is willing to pay. Just as an example, if you are risk averse, you’ll likely accept a price for your insurance which equals p*L.

If you don’t trust me, check on Internet the probability to have an accident (according to your age and kind of vehicle), and the average damage you can have. Multiply both factors and you’ll probably get what you pay annually for your insurance – plus obviously the benefit’s margin. If not, your insurance’s company probably believes you’re a risk lover!

Antonio González