¶ … Discount Scheme for Health Insurance No Claim Discount (NCD) Schemes are Frequency-rating systems and are commonly used in insurance. NCD schemes represent an attempt to categorize policyholders into relatively homogeneous risk groups who pay premiums relative to their claims experience. Those who have made few claims in recent years are rewarded with discounts on their initial premium, and hence are enticed to stay with the company (Boland, 2006). Depending on the rules in the scheme, new policyholders may be required to pay the full premium initially and then will obtain discounts in the future as a result of claim free years. The general insurance actuary modeling an NCD scheme would frequently use Markov chain methods to investigate how premiums and movements take place over time.

No Claims Discount scheme is a form of frequency rating used in health insurance; the practice is to consider the number of years since the last claim. One important condition for this scheme is that the insurer must be notified within a specified period of time upon the occurrence of any loss or damage by the insured.

NCD is expressed as a percentage of basic premiums. The basic premium is an amount dependent on the cover provided by the policy and on certain facts about the insurance, the policyholder and the policyholder's beneficiaries. Among the factors used in rating are the age of the insured, place of residence and whether a voluntary excess is required whereby the insurer is not liable for the first £X of every claim for the policyholder.

Effects of NCD

NCD discourages making of small claims and keeps claim costs and management expenses at a lower level than they would otherwise be. A policyholder contemplating whether to make a claim will usually recognize that claiming may sometimes result in a penalty through loss of future discount (Denuit, Marechal, Pitrebois, & Walhin, 2007). The total penalty is often somewhat arbitrary; it depends on the features of the particular N.C.D. system and the current position of the policyholder on the discount scale.

Furthermore, it is apparent that the claims history of an individual policy are not enable us to go far in correcting the premium for a policyholder for whom the risk differs...

Whilst this seems unsatisfactory, it may be regarded as inevitable in conditions in which there are only about 90 disallowed claims per 1000 frequencies in a year.
Calculation of penalties when the basic premium is $100

The No-claim discount scheme has 11 levels and all new customs start at level 0, where level 0 is the lowest lever and level 10 is the highest. The new entrants start at 100% of basic premium and move up or down by 20% on making a claim or not. Besides, the minimum premium is 40% of the basic premium. Any customer having no claim in the last year will be moved up one level, those with moderate claims move down one level and severe claims move individuals down 3 levels.

A points rating system is used in calculating basic premiums and points allocated for each value of the rating factors. Furthermore, the scale of premiums is multiplicative; the premium for T+1 total point is (1+k) times the premium for T. total points (Pinquet, 2012). Points scales in which an increase of 1 in the number of points corresponds to an increase in premium of 21/4% and 6% respectively. Some values of Vn are calculated below.

Premium increase of 21/4%

Premium increase of 6%

n

(47-n)

Vn

n

(18-n)

Vn

0

47

1.0000

0

18

1.0000

10

37

0.80051

4

14

0.79209

13

34

0.74882

5

13

0.74726

16

31

0.70047

6

12

0.70496

23

24

0.59944

9

9

0.59190

31

16

0.50169

12

6

0.49697

41

6

0.40161

16

2

0.39365

47

0

0.35142

18

0

0.35034

The above table shows values of n for which, at the given rates of interest, 100 (1-Vn)…