### 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…

### Pension Plans: DB vs DC

Broadly there are three sources of Retirement Income:
1.Government Programs (such as Social Security Benefits)
2.Employer Programs (such as Pensions)
3. Personal Savings

1. Governmental Programs: Under this program, there are Social security Benefits (Social Security benefits are paid out monthly to retired workers and their spouses who have, during their working years, paid into the Social Security system) Medicare and Medicaid. Difference between Medicare and Medicaid is that, Medicare is a federal program that provides health coverage if you are 65 or older or have a severe disability, no matter your income. Medicaid is a state and federal program that provides health coverage if you have a very low income

2.  Employer Contributions: For example: Defined Contribution plans, Defined Benefits plan etc. which we will discussed shortly.

3.  Personal Savings: such as Personal investments.

Now Let’s start: Various parties involved in pension schemes are as follows:
Employer, Trustees, Investment Managers, Actuary, Pension regulator.
Let’s Define Some Technical Jargons:
1.  What is a Pension Scheme? A pension scheme is an arrangement made to provide individuals with the regular income once they reach retirement age. Most common arrangements are Defined Benefits, Defined Contribution and Hybrid Plans.
2. What is a Contribution? Contributions are the regular or irregular payments made into the schemes by employees (by way of deduction from their payslips) and employer
3. What are the main type of benefits? A.) Monthly Pension B.) Commutation on Retirement (i.e. cash in lumpsum) C.) Lump sum on Death on service/retirement
4.What are type of members?
a.) Active: members who are still in employment and contributing to the scheme
b.) Pensioners:  members who have retired and are in receipt of pension.
c.) Deferred: members who have left employment but have not yet reached retirement age.

Defined Benefits: A defined benefit pension plan is a type of pension plan where the benefits are fixed and by benefits fixed we mean that the formula for calculating benefits is fixed. Here the employer promises a specified pension payment or Lumpsum upon retirement, that is determined by an Actuary appointed by the scheme based on the employees earnings history, tenure of service and age. Every year employer has to contribute to the pension pot (i.e. contribution). There are various formulas structure which varies from employer to employer, some of them are as follows:
1.Final Average Pay: Annual benefit will be: 2%*(Final 5-year average annual salary) *Years of service. Do not learn the numbers, but learn the format.

2.Career Average Benefit: Annual benefit will be: 1.5%*(Total Career earnings or average of participant’s career earnings). Do not learn the numbers, but learn the format.

3. Unit Benefit: Annual Benefit will be: 350*Years of service. Do not learn the numbers, but learn the format.

Note: To pay benefits employer set aside money in a trust that will be used to pay future benefits. Liabilities of DB plans are present value of all those promises that employer makes to his employees. Liabilities will represent the ideal asset value that an employer have put aside to payoff liabilities.

Defined Contribution: Unlike a Defined Benefit plan, here the contribution amount is fixed. A pension pot is built up using the employer and employee contributions. Unlike a Defined Benefit scheme,  the end benefit is not known in advance, but the monthly contribution to be made from both parties can be determined. It is more like an account balance and portable also which means that it can transferred from on employer to another or it can be paid at the time of termination in a lump sum. Here the employee bears the financial risk. These are of 3 types broadly:

1.401(k) plan: Annual Contribution: Employee contribution + Employer contribution (which may differ)

2. Profit Sharing Plan: Here the employer contributes around certain percentage of employee income. It keeps on changing year to year as it all upto employer discretion. In the year of higher profits, he may contribute more.

3.  Money Purchase Plan: Here annual contribution is fixed by employer; and employee contributes too.

Note:  Actuary not needed to determine contributions. Here the amount contributed by employer and employee and then invested accordingly. Here the plan assets equal to employee account balance which is same as plan’s liabilities because this is employer has to pay when employee retires.

 Basis DB DC Basis for determining benefit Uses known pay and service Uses unknowns such as investment returns Contributions come from Employer Employer and Employee Impact of Tenure on Benefit Based on years of service No impact. Risk Borne More by Employer Employee

As an Actuarial Consultant, what can you suggest to your client? Let’s see 2 different Cases
Q.) If client has issues of Labour Turnover and now they want to offer attractive benefits So, what should they do?
A.) They should go for Defined Benefit Plans as employees are encouraged to stay for longer period as benefit grows exponentially as the tenure with the company increases
Q.) If client starts his high-tech business and he wants to provide benefits to employees which can be portable (i.e. Transferrable) to another employer as well and can hire employees at any age, what should they do?
A.) They should go for DC plan here, as they can attract even a college graduate who is looking for employment. It allows employees to have an option of transferring their account balance to another employer. Even the mobile workforce valued the DC plan due to its portability.

Various Roles Played by Parties are:
Employer: The key role of an employer after set up a scheme and its design is to pay contributions into the scheme as determined by the deed, rules and actuarial advice (where relevant).

Actuary: The Actuary is appointed by the Trustees of Defined Benefit scheme. The actuary is responsible for monitoring the funding level of the scheme and recommending the amount of contributions due to the scheme to meet the required funding levels.

Investment Manager: They are appointed by Trustees to manage the investments as determined by the Trustees. The scheme can have a number of investment managers specialising in certain investment types ex: equities, bonds etc.