Dependence%20between%20mortality%20and%20morbidity:%20is%20underwriting%20scoring%20really%20different%20for%20Life%20and%20Health%20products?

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Dependence between mortality and morbidity is
underwriting scoring really different for Life
and Health products?
1.A. Stochastic Dependence 9.A. Various Topics

• Andrey Kudryavtsev,
• St.Petersburg State University, Russia

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Aim

• to show that underwriting scores are quite close
  to each other for different kinds of insurance
  products, say for life and health insurance
• If so, there are problems in portfolio
  construction because of
• risks may be more dependent,
• possible higher degree of risk accumulation

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Idea

• to compare underwriting scores for life and
  health risks of a sample population
• Results
• help to understand question how to use and
  interpret the underwriting scores
• do NOT help to solve any questions of statistical
  estimation

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Methodology

• The sample population used is investigated from
  medical point of view
• The medical records and reviews were used to
  produce the averaging underwriting scores for
  life and health risks
• The scores are comparing to estimate the
  existence and degree of correlations
• The idea of modelling with copula is analysed

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The investigation

• paper is based on the special study with data
  collection for real group of people
• The number of people studied was 769
• The study took place in 2000
• The basic aim of the study was mostly medical
• It included two parts
• deep medical investigation
• survey about peoples preferences in healthcare

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The place of investigation

• Lyssye Gory a small town in Central Russia in
  Saratov Region (downstream river Volga,
  south-east from Moscow)
• WHY
• typical agricultural province in Russia with some
  industrial development
• an appropriate professional mix of population

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The target group

• people living in one medical district
• additional restrictions
• age interval chosen (from 20 to 49 including the
  latter age)
• full set of the covariates (risk factors)
  investigated

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Reasons for age restrictions

• Young people (younger than 20 year old) are
  presumably completely healthy probably no extra
  life and health risks
• Old people (50) are probably quite ill the
  dependence observed between life and health risks
  is basically explained with poor health
• Only chosen age range (20 to 49) demonstrates
  balanced mixture of risk sub-groups

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The basic risk factor chosen

• job/profession (with additional information about
  working conditions)
• height/weight index
• existing conditions (current diseases)
• addictions (tobacco smoking and alcohol drinking)
• heredity factors (indirectly estimated)

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The Underwriting Manuals used

• Insurers
• Skandia International Insurance Corporation
• Munich Re
• Cologne Re
• There are some differences in those
  company-specific scoring procedures
• Resulting score was equal to arithmetic average
  between company-specific scores (all three
  manuals for life score and Skandia and Cologne Re
  manuals for health score)

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Underwriting scoring

• Risks estimated
• Life (extra mortality score under whole life
  insurance contract )
• Health (permanent health (income protection)
  insurance with 4 weeks of waiting periods)
• The choice of health scoring
• it shows quite serious problem with health
• too serious (very long) diseases are rare

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Rounding the individual scores
13
The distribution of people investigated
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The distribution of people investigated

• there is some form of dependence
• the coefficient of correlation is 0,6312
• quite large the actual t-test value is 24,6
  that is much higher than the critical value
• nevertheless, it is far from comonotonic
  (one-to-one functional) dependence
• the dependence could not be explained only with
  mortality risks in permanent health (income
  protection) products as it is too high

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Standard/sub-standard proportions
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Standard/sub-standard dependence conclusions

• there is large enough dependence between life and
  health scores
• even for age intervals where it is not highly
  expected from the point of view of health
  dynamics with age
• actuaries and underwriters should be more careful
  with assumptions about the existence of
  independence between different Life and Health
  products in context of ALM and similar concepts

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Standard/sub-standard dependence analysis

• The important result is that the proportion of
  standard risks is 27,5 per cent for life score
  and 22,69 per cent for health score
• It is too small
• The odd of standard and sub-standard risks (13)
  is different from usual odd for life insurance
  portfolios (91)

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Standard/sub-standard dependence explanations

• The differencies could be explained with
• more conservative estimation under the
  investigation than one in insurance practice
• self-selection of potential clients with poor
  health
• full informational support in the investigation
  vs. informational deficit in practice of
  insurance
• The latter explanation is important for insurance
  practice

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Dependence amongsub-standard risks

• Correlation coefficient is 0,84
• It is even more than for all risks
• The idea is to develop more formal model than
  simple statistical coefficient, say, copulas
• It helps to understand the character of
  dependence in more details

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Marginal distributions

• They are conditional as the risks analysed are
  sub-standard
• The last two boxes (300 and gt300) for health
  risk scores should be combined
• Both distributions were fitted using Maximum
  Likelihood method
• In both cases, the best goodness-of-fit (measured
  with ?2-test) was achieved on
• Log-Normal distribution

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Marginal distributions
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Copula

• As a first choice, the normal copula could be
  used
• where is the bivariate Normal
  distribution function with zero vector of
  expected values and covariation matrix

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Copula conclusions

• As marginal distributions in our case are
  Log-Normal, the copula simply gives the bivariate
  Log-Normal distribution
• Unfortunately, the model is not well calibrated
• Other copulas tend to bring much more complex
  formulas
• Such models may be quite simple tools for
  portfolio modelling in the context of ALM or
  similar concepts

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Thank You!