### Role of Generalised Linear Model in non-life pricing Phase3

Phase1: http://www.actuarysense.com/2018/10/role-of-generalised-linear-model-in-non.html
Phase2: http://www.actuarysense.com/2018/11/role-of-generalised-linear-model-in-non.html So we know that the purpose of GLM is to find the relationship between mean of the response variable and covariates.

Linear Predictor: Let’s denote it with, “η” (eta). So, linear predictor is actually a function of covariates. For example, in the normal linear model where function is Y = B0 + B1x. So linear predictor will be η = B0 + B1x. Always note that linear predictor has to be linear in its parameter. In this case parameters are B0 and B1. But still the question is how I came up with B0 + B1x as a function? First of all, note that broadly there are two types of Covariates. 1. Variables: It takes the numerical value. For example: age of policyholder, years of ex…

### Deterministic Model:

• Here the output of the model is fully determined  by the parameter values and initial conditions. This model assumes that its outcome is certain if input is fixed. No matter how many times one recalculates, one obtains exactly the same result.

Example:
• Good example is Linear programming. If we want to minimize the cost by selecting the decision how you want to transport the goods from one place to another , then you are dealing with deterministic model for every data.

### Stochastic Model:

• Stochastic models possess some inherent randomness. The same set of parameter values and initial conditions will lead to different outputs. Every time you run the model , you will get the different result.
Example:
• When you roll a die, you will get different results.

Note:
For Building a stochastic model
Create the Sample space — a list of all possible outcomes,
Assign probabilities to sample space elements,
Identify the events of interest,
Calculate the probabilities for the events of interest.