### Pricing of Insurance Products using Bayesian Statistics

Hello Everyone, in our last topic we discussed what Bayesian Statistics is?

if you haven’t read it, then please read that first. Here is the link:

So, for a Bayesian Statistics to reach in Insurance industry for actuaries, it has to gone through to Credibility Theory concept which is also based on Bayesian Statistics. So, let’s See what is credibility theory?

Suppose a local authority in a city wants to insure its 12 buses for the coming year claims arising from accident involving these buses. Data of past 4 years show that average cost of claim per annum for a bus is $1500 (this is your own data).

So let me give additional information too: We have data relating to a large number of buses from all over the country say US and the amount is $2500 (this is outside/collateral data).

I am assuming as of now that we don’t take loading into consideration for calculating premium.

So now, there will be extreme cases of Premium:

*: As an insurer I will charge $1500 because this estimate is based on the most appropriate data*

__Case-1__*As an insurer I will charge $2500 because this estimate is based on most data.*

__Case-2:__
Then there comes a credibility theory which says that you can take the weighted average of both of them.

Premium = Z*1500 + (1-Z)-2500 here “Z” is the credibility factor.

The larger the value of Z is, the larger you are putting interest in your own Data.

Seems easy, I guess. Let’s see now its role in insurance:

Example-1: Suppose as an insurer i want to insured the damage caused by falling Satellite dishes (Tata Sky, DTH etc.) but I don’t have enough data available with me to judge my premium accurately. Then what I will do is to find the appropriate collateral data (i.e. Outside Data) say TV Aerials (Dish Antennas etc.). So, you can see here that to refine my estimate I can use the outside information to refine my estimate using my own data too. What I will be doing here is to calculate premiums using both the information but the weightage I will give more to Collateral data my own data is very less/scarce as of now.

So as the company sold more of new policies, the pattern for satellite dishes become clearer and insurer could put more emphasis on direct data and our Z value will keeps on increasing.

Will talk about it’s in Reserving in next Topic.

But before that let me ask you two simple questions:

Q.1 : What will be the value of Z in case of Chain Ladder Method?

Q.2: What will be the value of Z in case of Expected Loss ratio method?

Will discuss various techniques of reserving and its role by Bayesian and Credibility in our next topic.

Thanks and Regards, Yours Truly

Kamal Sardana

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