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Showing posts from September, 2018

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…

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…