Chapter 19 Pricing (1) Individual business

Question 1

The stages involved in process of calculating risk premium for PMI

Answer 1

• choose a base period over which to collect claims and exposure data
• collect data, checking the accuracy and appropriateness of data
• split data into homogenous groups
• calculate historical burning cost premium for each group
• analyse data eg identify trends - Analyse freq ,amp; sev & exposure separately
• adjust and project forward to obtain future risk premiums.

Question 2

Factors considered when selecting base period

Answer 2

• volume - long enough to have credible data
• detail - where claims variable, a lot of data is needed.
• trends - period should be long enough to identify trends.
• relevance -
• unknowns - ideally we want most recent data.

Question 3

Burning cost premium (BCP)

Answer 3

• a common starting point in calc of risk premium is burning cost
• BCP is the true past risk premium of an actual portfolio of data ie actual cost of claims incurred per policy or per unit of exposure
• BCP = Claims / total exposed to risk

or BCP = Avg claim amt * Claim incidence rate

Question 4

Adjusting based values

Answer 4

-Unusually heavy/light experience in base period - either aggregate more years to make experience more
typical.

-Large or exceptional claims - decision needs to be made as to whether these claims are truncated or left in the data.

-Trends in claims experience - more weight should be given to most recent period if trends are identified.
Investigate if trends are likely to continue.

• Changes in risk - these may appear as trends and can be dealt with as trends. Or insurer should project risk elements separately.
• Changes in cover -if cover changes these should be allowed for in projections.
• changes in the cost of RI
• Seasonal variation in claims - claims varying over the year.
• incomplete claims - late reported claims
• change in agreements with suppliers - eg lower tariffs in new period ahead.

Question 5

Projection base values

Answer 5

• We need to project past claims costs into the future allowing for :
• changes in policyholders profile by benefit options
• claims inflation
• trends
• other changes in cover

Question 6

Time periods involved in the projection

Answer 6

• period of exposure containing the base experience
• period during which policies will be written under new premium rates
• full period of exposure covering all the claims that can arise from the policies written under the new rates.

Question 7

Allowance for inflation

Answer 7

• the projections need to allow for the expected inflation between
• the mean payment date of claims in base period
• and the mean payment date of claim arising during the exposure period of new rating series.

Question 8

PMI : Taking risk class of policyholders in account

Answer 8

-Risk premium(age,gender) = Sum( i(k) * ACk)

where i(k) is incidence rate for benefit k
ACk is the average claim cost  for benefit/procedure k.

Question 9

PMI: The risk premium should be adjusted for which other loadings?

Answer 9

• Investment income
• contingency loadings
• Other considerations: risk premium may be adjusted for excesses, the presence of a no claims discount

Question 10

Cash plans pricing

Answer 10

• Similar to PMI except the cost of claim of some benefit classes is defined with a fixed amount per treatment, or per day of care.
• For the latter will need to estimate expected number of days of treatment in order to calculate ACk.
• These policies will often have a coinsurance or excess element.
• Difficulties can arise in establishing age estimate on which to determine a flat rate. This is because rate of premiums are flat over broad age ranges but incidence rates may vary significantly by age.
• Total calculate needs to be adjusted to take account of intertia. This arise because:
  1. people take cover thinking of one benefit not others covered by same policy.
  2. benefit might be so small policyholders do not claim. or forget to.

Question 11

Accidental death and total permanent disbility

Answer 11

• Similar to PMI and cash plan, may have some experience rating.
• premium = incidence rate * sum insured

Question 12

CI incidence rates

Answer 12

-We calculate different incidence rates for different critical illnesses.

• i(x,d)
  this is the incidence rate at age x cause by illness d.
• d may include:
• hd - heart disease
• s - stroke
• c-cancers
• o - other causes

i(x) = i(hd,x) + i(s,x) + i(c,x) + i(o,x)

-overlaps arise when more than one allowable CI cause underlies same individual claim.

Question 13

Accelerated CI incidence rates

Answer 13

-a relative approximatoin for risk premium rates for an acceleralted CI policy is derived below:

ix + [1-k(x)]*q(x)

• where ix is the CI incidence rate
• k(x) is the proportion of deaths due to CI
• q(x) mortality rate

Question 14

Stand-alone CI insurance incidence rate

Answer 14

• i(x)*( probability of surviving the survival period)
• These formula are applied each CI definition separately and then combined to provide overall risk premium for CI cover.

Question 15

LTCI incidence rates

Answer 15

-Multiple-state or inception/annuity methods can be used to value the benefits.

Question 16

Modelling Complexities: PMI

Answer 16

• Modelling is complicated by
• the existence of NCD multi-states (for healthy lives) where applicable
• the need to incorporate the reclaim of initial costs over several renewals in the pricing model
• the need to model the chain of occurrence through GP referral via specialist to hospital, plus the delay to settlement.

Question 17

PMI complexities: It is necessary to estimate

Answer 17

• it is necessary to estimate
• distribution of claims frequency, difficulty in defining a discrete claim.
• frequency parameters are dependent on duration on policy inception, age, gender, time of year, occupation.
• distribution of claim amount, indemnity often without ceiling.
  
  • distribution of claim amount is dependent on hospital capacity, inflation , medical science progress.

-impact of sales tax on future growth.

Question 18

Data limitations: PMI

Answer 18

• There are likely to be the following data issues :
• an absence of insurance statistics
• problems with family covers where details of individuals on risk may not be known.
• problems with group arrangements similarity, where details of individuals can only be estimated.

Question 19

Modelling complexities: CI

Answer 19

-It will be necessary to estimate theoretically up to forty different distributions, if each covered condition is modelled separately, plus allowance for future trends.

• possible use of separate approaches for disease-based and treatment-based
• guaranteed and reviewable alternatives

Question 20

CI influence modelling complexities: Other influences on claims distributions

Answer 20

• advancements in medical science which will impact cures
• earlier diagnosis
• simpler and more readily available operations.

Question 21

CI: data limitations

Answer 21

-statistics provide help with historic incidence - however practically, only cancers and heart attacks are likely to provide enough data.

Question 22

LTCI complexities: it will be necessary to estimate?

Answer 22

-distribution of claims frequency - little experience on which to estimate future transition rates

• distribution of claim amount, could place cap on weekly/monthly benefit, but otherwise little control.
  
  • distribution is dependent on economy, inflation, & capacity

-demand, this is very dependent on political commitment.

Question 23

Data limitations: LTCI

Answer 23

-an absence of insurance statistics.

Question 24

Other issues which may complicate modelling

Answer 24

• the role of genetics
• trends in anti-selection
• the quality of underwriting