Chapter 19: Pricing (1)

Question 1

Describe thestagesinvolved in calculating therisk premium for PMI

Answer 1

choose a base period over which to collect claims and exposure data

data should be of sufficient volume to include trends, however should not introduce excessive heterogeneity due to changes over time

collect data

split data into homogeneous groups, ensuring each cell has enough data to be credible (may have to combine smaller cells to ensure credibility)

adjust the data for:
unusually heavy/ light experience
large claims
trends in claims experience
seasonal variation in claims
IBNR
changes in cover (benefit enhancements/ reductions)
changes in agreements with providers
pastinflation

calculate historical burning cost premium for each benefit option:
risk premium = sum ( i_k * AC_k)
where i_k is the claim incidence rate for treatment k , and AC_k is the average cost of claim for that treatment
important to consider anyproduct specific features such as excesses and co-payments

project the BCPs forward allowing for:
changes in policyholder profile by benefit option
renewal rates, new business expectations
claims inflation
futurechanges in cover (benefit enhancements/ reductions)
long term trends in claim experience

insurer will have to allow for loadings:
expenses (includes overheads), commission, reinsurance, solvency/ contingency (allowing for uncertainty)/ profit margins, investment expenses

other considerations:
competitiveness, cost of meeting solvency capital requirements, regulatory restrictions, PRE, sensitivity testing (given level of actuarial judgement used in making adjustments)

Question 2

Explain the claim incidence rates derived for standalone CI with survival period and accelerated CI

Answer 2

overall critical illness incidence rate may be the sum of incidence rates for different critical illnesses

consider overall critical illness incidence rate for policyholder age x:
i_x = (i^heart disease)_x + (i^stroke)_x + (i^cancers)_x + (i^other)_x

accelerated CI:
claim incidence rate = i_x + (1-k_x)*q_x

i_x: (overall) critical illness incidence rate
k_x: proportion of deaths over [x, x+1] due to critical illness
q_x: mortality rate

stand-alone CI, with survival period:
claim incidence = i_x * (1-q_x)

Question 3

Discussmodelling complexitiesfor healthcare products

Answer 3

claim incidence rates:
PMI - depend on many factors and there may be difficulty in defining discrete claims
CI - may be necessary to estimate theoretically up to 40 different distributions
LTCI - lack of (industry) data

claim amount:
difficulty modelling indemnity claims - PMI and LTCI

data limitations:
PMI - details of individual risks may not be known for family covers
CI -general lack of data for all illnesses excluding cancer and heart attacks

other:
PMI -difficulty in defining discrete claim, need to model claim chain (PMI)
CI -disease-based vs treatment-based claims
LTCI - the use of multi-state models

Question 4

Write down the formula for calculating the premium with loadings question

Answer 4

P = risk premium / (1-[sum of loadings])