CREDIBILITY THEORY

OUTLINEToday’s session will coverIntroduction to credibilityCredibility theoryCredibility premium formulaCredibility factorProperties of credibility factorBehavior of credibility factorOur future prospective

INTRODUCTION

Credible : believable /good enough to be effective;

Credibility: the state or quality of being credible;In statistics:

Credibility is a statistical estimate; Refers to the degree of trust.

WHY DO WE NEED “CREDIBILITY”?

Determination of premiums in insurance sector;Observation of a result yields only an estimate of the

“truth”;How much can we believe in our data?

WHAT IS CREDIBILTY THEORYCredibility theory is a technique that

can be used to determine premiums or claim frequencies in general insurance;

Credibility theory uses mathematical models and methods for making experience-based estimates, in which “experience” refers to historical data.

GENERAL TERMSMONETARY: related to money; COMPENSATION: something that is given to make

up for damages, losses etc;MONETARY COMPENSATION: money give to

make up losses, damages etc.

GENERAL TERMS(CONT…) INSURANCE: An agreement in which a person

makes regular payments to company and the company promises to mitigate it in exchange for monetary compensation for death or injury.property loss, damagesbusiness loss etc.

GENERAL TERMS(CONT…)PREMIUM : The amount paid for insurance;CLAIM: The amount of money that a person receives

from an insurance company.

Average cost of claims from previous years

for insuring bus 1600₹

Weighted average of these two

Average cost of claims of similar buses from

previous years ₹ 2500

CREDIBILITY PREMIUM FORMULA

Z is known as Credibility factor . is an estimate of number of claims based on data from

the risk itself.μ is an estimate of the expected number of claims based on collateral data.the value of Z lies between 0 and 1.

PROPERTIES

The credibility factor Z is just a weighting factor;

Its value reflects how much trust is placed on the data from the risk itself ( ) compared with the data from the similar group (μ).

PROPERTIES(CONT…)

Value of the credibility factor Z should reflect the amount of data available from the risk itself, not the actual data of the risk itself.

If Z were allowed to depend on then any estimate of number of claims say ϕ,could be written in the form of by choosing Z to be equal to

(ϕ – μ)/( – μ)

PROPERTIES(CONT…)Because

BEHAVIOR OF Z

The more the data from the risk itself, the higher should be the value of the credibility factor Z.

The more the data from the collateral data, the lower should be the value of the credibility factor Z.

CALCULATION OF CREDIBILITY FACTOR

Three approachesLimited fluctuation approachBühlmann approachBayesian approach

FUTURE PROSPECTIVESWidely discuss about three approaches:

Limited fluctuation approachBühlmann approachBayesian approach