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Showing posts from December, 2017

### 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…

### What is Immunization and Explain its 3 conditions ?

IMMUNISATION: Definition:  Immunisation is a strategy of managing a Portfolio of Assets such that business is immune to interest rate fluctuations. In other words, it is a process where an investment manager select an asset portfolio in such a way that his surplus (Present Value of Asset-Present Value of Liabilities) is protected against change in interest rate.
Background: During early 1900’s we usually saw our portfolio changes due to changes in our cashflows but then there was an increase in interest rate volatility due to which we started seeing the change/impact on our portfolio due to change in interest rate.
3 conditions: 1)VA(i0) = VL(i0) which means Present Value of Assets = Present Value of Liabilities.
Suppose we have to pay Rs.10,000 after 2 years, so what we can we do is purchase 2 year Zero coupon bond whose mat…

### Concept of Convexity

Convexity
Definition: Convexity describes how much a bond's duration changes when interest rates change ·Where the cashflow series have payments coming Close to each other will have a lower convexity. ·Where the Cashflow series payments is more spread out over time will have a higher convexity.

·Now let’s Consider three cases 1.There is a zero-coupon bond of say 20 years 2.There is a bond having cashflows at time 3 and at time 10 3.There is a bond having cashflows at time 1,2, 3,….,11,12
ØNow Zero coupon bond will have lower convexity because it consists of just one payment. But in 3rd case convexity is high because payments are spread out over a longer period of time. ØIn Technical Terms , let’s say X is the present value of all cashflows. So take the double derivative of X with respect to change in int…

### Brief Information about Health Insurance

General Insurance:Broadly, General insurance is divided into 3 Categories i.e. 1.Personal Insurance 2.Liability Insurance 3.Property Insurance Personal Insurance has 2 major aspects i.e. 1.Mediclaim Policies 2.Personal Accident Policies

Mediclaim Policies: Introduced in India in 1981. They offer Health insurance and can be issued as Individual policies or as a Group Policy.
Health Insurance: ·It is a type of insurance coverage that covers the cost of an insured individual's medical and surgical expenses. Depending on the type of health insurance coverage, either the insured pays costs out-of-pocket and is then reimbursed, or the insurer makes payments directly to the provider. ·A Health Insurance policy reimburses the insured for medical and surgical expenses arising from illness or injury that leads to hospitalization

Inclusions: Following expenses are reimbursed 1.Nursing expenses, Anaesthesia and other specialist doc…

### The Dilemma of Duration

Before going to the concept of Duration and related terms lets see what is YTM = Yield To Maturity

Yield To Maturity :The Yield to Maturity for a Coupon Paying Bond has been defined as the effective rate of interest at which the discounted value of proceeds of a bond equals the price.Now let's Come to Duration
Background: An Investor is concerned whether his assets in a portfolio are sufficient enough to fund the liabilities or not. So for portfolio with investments in Fixed interest securities investor is more concerned in knowing the change in its portfolio due to change in its interest rate.Now for simplicity, suppose interest rate will remain same throughout the term of a security.

Effective Duration: also known as Volatility. It measures sensitivity in cashflows due to change in interest rate. Let X be the present value of Payments at rate YTM. So Effective duration is the change in the X  with respect t…

### What is the difference between Select Mortality and Ultimate Mortality?

ULTIMATE MORTALITY:
A simple life mortality table classifies people by attained age and assumes each attained age (or possibly age range) is subject to some rate of mortality. Another way of saying this is the mortality depends on only one variable, attained age.

SELECT MORTALITY: Since most life insurance involves some kind of underwriting or selection process, it may be interesting to look at the mortality based on two variables, age at selection and duration since selection. This produces a two-dimensional table; that table is Select mortality table.

NOTE: ·A select mortality table includes mortality data on individuals who have recently purchased life insurance. These individuals tend to have lower mortality rates than individuals who are already insured, due chiefly to the fact that they have most likely just passed certain medical exams required to obtain insurance.·some period of years after the selection (say…

### What is Random Variable?

Random Variable: When there is a probability associated with a variable that makes it Random Variable. So a Random variable can take many different values with different probabilities.
Example: Q.1) No. of Days in a week-: Is this a Random Variable?
A.1)  NO, because no. of days in a week is fixed i.e 7

Q.2) No. of Days in a Month-: Is this a Random  Variable?
A.1)  Yes, because no. of days in a month can be 28,29,30 or 31. So this is Random in nature.

Note:
Suppose X is "Something" now it can take value "0" if 3 comes up on a Dice and "1" if even no. comes up on dice.
So we know that probability of getting a 3 on Dice is 1/6 . So probability of getting a value "0" is 1/6 Similarly the probability of getting an Even no. on dice is 1/2. So probability of getting "1" is 1/2.
so we see that when "something is attached with different values along with different probabilities it becomes a Random variable.

### Differentiate between Stochastic and Deterministic model ?

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 i…

### Briefly discussion on Indian Insurance market ?

LIFE INSURANCE: First Life insurance company :
The Oriental Life Insurance company established in 1818. This was a British Company. The first Indian Insurance company was Bombay Mutual Life Assurance Society established in 1871.

When Does it Nationalize:
Nationalized on January 19, 1956. There were 154 domestic insurers,16 foreign insurers and 75 Provident funds that were taken by central government ; all the 245 insurers and provident funds result into a company named as Life Insurance Corporation of India(LIC) with a capital of Rs.5 crore by Government of India.

Follow us on LinkedIn : Actuary Sense Follow me on LinkedIn: Kamal Sardana GENERAL INSURANCE: First Non life Insurance Company:Triton Insurance Company ltd. was formed in 1850 in Kolkata by British. The first Indian general insurer was Indian  Merchantile Insurance Company formed in 1907.
When Does it Nationalize:
Nationalized on November 22, 1972. All the 107 Indian and Foreign insurers operating were nationalized and grou…

### Endowment Plans Vs Term Insurance - Which insurance plan is better?

Both Term Insurance and Endowment plans are traditional life insurance plans. Both offer comprehensive life coverage and are good tax-saving instruments.

Which one is better will be concluded at the end but note the differences:
If you buy a term plan, the beneficiaries will receive the guaranteed death benefit only in case of your death within the stipulated time. But in case of an endowment plan, you will receive the entire sum assured along with bonuses that you have built over time, once the policy tenure is over. Under Endowment if you died in between the time your beneficiary get the payment. So Term is a pure life insurance policy an endowment plan, on the other hand, is a combination of investment and insuranceInsurance agents are not much inclined to sell a term plan because the sales of endowment plans get them higher profits.A term plan offers comprehensive life coverage at very low premium rates. For the same amount of coverage, an endowment plan will charge higher and if …

### Difference between Estimate and Estimator ?

Estimator: It is a Random Variable. So its value depends on the outcome of some experiment, and it has a statistical distribution.
Estimate: It's value is Constant. It is the value taken by an estimator, given a particular set of sample data.

Note: One ESTIMATE will never give you multiple ESTIMATORS but one ESTIMATOR will give you multiple ESTIMATES.ESTIMATOR can be a good or bad, but ESTIMATE can never be good or bad.