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### Role of Generalised Linear Model in Non Life Pricing - Phase1

We will cover a series of topics relating to how Non Life Pricing is done through GLM.

But first let's see what is GLM

Let’s take the example of Weight (Y) and Height (X). The aim of linear models is to find the line of best fit through the data points.

Here is your X axis is Height and Y axis is your Weight. Y = B0 + B1x

Line of Best Fit is B0 + B1x where B0 is intercept on Y axis and B1 is the gradient.

Now the question is how that line comes?

Well, line is chosen in such a way to minimize the sum of squared error terms where error terms are distances from data points to straight line, error terms are normally distributed with mean 0 and variance σ2.

2.

We can extend our model to allow for other predictive variables. For example, we can decide that Weight can depend on height and calories consumed per day both. So here we cannot find the line of b…

But first let's see what is GLM

**Generalised Linear Model**Before Jumping on to what is GLM, let’s see what is**Linear models**1.**:***Linear Models*Let’s take the example of Weight (Y) and Height (X). The aim of linear models is to find the line of best fit through the data points.

Here is your X axis is Height and Y axis is your Weight. Y = B0 + B1x

Line of Best Fit is B0 + B1x where B0 is intercept on Y axis and B1 is the gradient.

Now the question is how that line comes?

Well, line is chosen in such a way to minimize the sum of squared error terms where error terms are distances from data points to straight line, error terms are normally distributed with mean 0 and variance σ2.

2.

**:***Multiple Linear Regression*We can extend our model to allow for other predictive variables. For example, we can decide that Weight can depend on height and calories consumed per day both. So here we cannot find the line of b…

### CFM vs UDD vs Balducci

Life Tables: It is a computational tool based on a specific survival model. Our
task is to generate a survival model and our output will be a life table. Life
table is based on Unitary method. lx= Expected no. of lives at age x dx= Expected no. of deaths between exact age x and exact
age x+1 NOTE: We call it expected and not actual because most of the values
will be in decimal too, so how can it be actual.

1.CFM ·It assumes that the force of mortality is constant, i.e. ux+t = ux ·If the force of mortality of a newborn is constant, it means that the expected future lifetime of this life is 1/μ no matter what age he is in. ·Survival Function in this case will decrease exponentially. ·If 0<s<t<1 then t-spx+s = tpx/spx …

*But there is a limitation of Life Tables:*It is defined only for integer ages. If we have to calculate probability of death/survival at any non-integer age we will use 3 assumptions: 1.**CFM=**Constant Force of Mortality 2.**UDD=**Uniform Distribution of death 3.**Balducci assumption**1.CFM ·It assumes that the force of mortality is constant, i.e. ux+t = ux ·If the force of mortality of a newborn is constant, it means that the expected future lifetime of this life is 1/μ no matter what age he is in. ·Survival Function in this case will decrease exponentially. ·If 0<s<t<1 then t-spx+s = tpx/spx …

### MWRR vs TWRR which is better and Why ?

We can decide between various projects that which one
is better and which one is not on the basis of different criteria such as: NPV, IRR, DPP But how can we measure the investment performance?
Well, there are basically three measures of investment performance: 1.Money
Weighted rate of return (MWRR) 2.Time
Weighted rate of return (TWRR) 3.Linked
internal rate of return (LIRR)

It is necessary to measure the performance of a fund which can be a pension fund, funds of an insurance company or funds of an asset management company. It is important for those who are responsible for the investment funds for example: trustees in case of pension fund will monitor how fund is performing i.e. they find out the rate of return of the fund and then compare it with performance of other funds. Before looking at different measures, let’s see some definitions: a.)Income generate by fund: it includes interest payments, dividends received fr…

**Follow us on LinkedIn : Actuary Sense****Follow me on LinkedIn: Kamal Sardana**It is necessary to measure the performance of a fund which can be a pension fund, funds of an insurance company or funds of an asset management company. It is important for those who are responsible for the investment funds for example: trustees in case of pension fund will monitor how fund is performing i.e. they find out the rate of return of the fund and then compare it with performance of other funds. Before looking at different measures, let’s see some definitions: a.)Income generate by fund: it includes interest payments, dividends received fr…

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