Chapter 19 Pricing (1) Individual business Flashcards
-Understand and apply techniques used in pricing health and care insurance in terms of: -equation of value & formula approach -cashflow techniques -describe principal modelling techniques appropriate to health & care insurance.
The stages involved in process of calculating risk premium
- 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 & sev separately
- adjust and project forward to obtain future risk premiums.
Factors considered when selecting base period
- 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.
Burning cost premium (BCP)
- 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
Adjusting based values
-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.
Projection base values
- 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
Time periods involved in the projection
- 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.
Allowance for inflation
- 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.
PMI : Taking risk class of policyholders in account
-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.
PMI: The risk premium should be adjusted for which other loadings?
- Investment income
- contingency loadings
- Other considerations: risk premium may be adjusted for excesses, the presence of a no claims discount
Cash plans pricing
- 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.
Accidental death and total permanent disbility
- Similar to PMI and cash plan, may have some experience rating.
- premium = incidence rate * sum insured
CI incidence rates
-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 allwable CI cause underlies same individual claim.
Accelerated CI incidence rates
-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
Stand-alone CI insurance incidence rate
- 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.
LTCI incidence rates
-Multiple-state or inception/annuity methods can be used to value the benefits.
