Showing posts from April, 2018

Role of Generalised Linear Model in non-life pricing Phase3

Before reading this article, make sure that you read phase1 and phase2. Here are the link:
Phase2: 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…

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.
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 …