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Role of Generalised Linear Model in non-life pricing Phase3

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Before reading this article, make sure that you read phase1 and phase2. Here are the link:
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.

In this Article we are going to talk about Linear Predictors.
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…

Role of Generalised Linear Model in Non-Life Pricing - Phase 2

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Before reading this article, make sure that you have read the phase 1.
Here is the link for the same:  http://www.actuarysense.com/2018/10/role-of-generalised-linear-model-in-non.html
In this Topic we will talk about Link function and Linear predictors.
We saw in previous topic that exponential family is
f( y; θ, φ) = exp[{(yθ – b(θ))/a(φ)} – c(y, φ)] where θ is your natural parameter and φ is your dispersion parameter.
Response distribution can be Gamma, Binomial, Lognormal, Poisson, Normal or Exponential and then we make it in the form of exponential family.
Now the thing is that relationship between Response and covariates is defined through mean of response distribution i.e. E[Y]
Let’s take the example of linear model where we defined Y = B0 + B1x. (learn about linear model in the previous topic),
Y – N ( µ, σ2) where your µ = B0 + B1x.
Now note one thing always that purpose of GLM is to find the relationship between mean of the response variable and covariates.
Photo credits: bajaj…

Role of Generalised Linear Model in Non Life Pricing - Phase1

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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

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…

Explanation of Motor Insurance

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Motor Insurance or Vehicle Insurance: Motor insurance is an insurance policy that protects the owner of the vehicle against any financial loss arising out of damage or theft of vehicle.
Motor vehicle coverage also includes damage caused to third party or property.
Motor Insurance is mandatory in India.
Motor Insurance is available for both cars and two wheelers. Now the premium will be lower for two-wheeler as compared to Car wheeler, as we know the more the sum insured, the more will be the premium, keeping all things constant.
Generally there are two types of Vehicle Insurance: 1.)Third-Party Car Insurance 2.)Comprehensive Car Insurance
Third Party Car Insurance: 1.Provides coverage against any legal liability arising out of injuries to a third party when the policyholder is at fault. 2.Third party cover does not pay for repair of damage to your car or if you suffer any car-related injuries. 3.It is mandatory for every motor vehicle owner to buy at least third-party insurance coverage in In…

What exactly is Brownian Motion

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Today we will talk about Brownian Motion, More than 60% of CT8 syllabus moves around Brownian Motion.
What is stochastic process: Stochastic process is a sequence of some quantity where the future values cannot be predicted with certainty.

Brownian Motion:
Definition: It is a stochastic process with a continuous state space and in continuous time. This process has stationary, independent and normally distributed increments.
Understanding: Here in CT8 we are going to model the share prices that is we are looking at how can we make share prices models so that we can predict our future returns on the basis of risk level decided by investor and then invest accordingly. Brownian motion is one of the tool with the help of which we can do this. Standard Brownian Motion has normal distribution which means it follows normal with mean “0” and Variance “t” at time t. Under the General Brownian, it also follows the normal distribution with mean “u” and variance “σ2” but these mean and variance are link…

How an Actuary calculates Expense for Pension Fund

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Let’s see some Actuarial Terminologies from Accounting Valuations point of view under US GAAP/IAS 19R: 1.Accumulated Benefit Obligations (ABO): ABO is an approximate amount of a company's pension plan liability at a single point in time. ABO is estimated based on the assumption that the pension plan is to be terminated immediately; it does not consider any future salary increases. Changes in annual ABO are mainly determined by changes in service costs, interest costs, contributions by plan participants. 2.Projected Benefit Obligation (PBO): A pension's projected benefit obligation (PBO) is an actuarial liability equal to the present value of liabilities earned and the present value of liability from future compensation increases.  Note: ABO differs from PBO as ABO does not includes any assumption about future compensation levels. For plans with flat benefit or non-pay related pension benefit formulas, the ABO and PBO will be same.

Today we will see Accounting Valuation through US …

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