Chapter 15: Quantifying uncertainty in reserves Flashcards

1
Q

9 Random factors influencing the run-off of claims reserves

A
  • the OCCURRENCE and SEVERITY of claims
  • levels of claims INFLATION
  • changes in the mix of claim TYPES
  • the notification DELAYS on individual claims
  • changes in claims HANDLING
  • legal changes that affect the size of awards
  • legal changes that affect the “heads of damage” awarded
  • court rulings on liability or quantum of individual claims not foreseen by claims handlers or not in the historic data
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2
Q

“Heads of damage”

A

Types of loss recognised in compensation awards for serious injuries, such as loss of income, medical and nursing costs, etc.

Awards due to:
- loss of income
- nursing costs
- pain and suffering

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3
Q

Further uncertainties in using historic data to project the run-off of claims (3)

A
  • The historic data only provides a limited sample
  • The quality of data may have varied over time.
  • “model uncertainty”
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4
Q

4 Terms used to identify the sources of uncertainty

A
  • Parameter uncertainty
  • Process uncertainty
  • Model error
  • Systemic error
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5
Q

Process uncertainty

A

The uncertainty in what the future outcome will be.
This is the randomness of the underlying process.

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6
Q

Parameter uncertainty

A

The uncertainty in selecting parameters within the reserving process, and hence the results.

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7
Q

Model error

A

The error/uncertainty arising from the fact that we might select an inappropriate model to derive our reserve estimates.

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8
Q

Systemic error

A

The uncertainty arising from unforeseen trends or shifts away from the current claims environment.

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9
Q

3 Types of ranges that might be used

A
  • range of best estimates
  • range of possible outcomes
  • range of reasonable / probable / plausible outcomes
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10
Q

“Range of possible outcomes”

A

This would represent the actuary’s estimate of the complete range of outcomes for future claims.
It would be considerably wider than the range of best estimates.

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11
Q

“Range of reasonable / probable / plausible outcomes”

A

This would typically be wider than a range of best estimates, but narrower than the range of possible outcomes,
… since it would allow for outcomes that cannot reasonably be regarded as an estimate of the mean or average outcome.

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12
Q

Stochastic claims reserving can be used to: (6)

A
  • assess reserve adequacy
  • compare different estimates and datasets
  • monitor performance
  • allocate capital
  • provide information to investors
  • facilitate discussions with regulators
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13
Q

2 Advantages of using the “Alternative sets of assumptions” method

A
  • It is simple to perform on deterministic or stochastic models
  • We use judgement when we select possible parameters. We can therefore allow for atypical volatility in the historical data.
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14
Q

3 Disadvantages of using the “Alternative sets of assumptions” method

A
  • We assign no explicit probability to each set of parameters.
  • We ignore model uncertainty using this method
  • We do not allow for process uncertainty if we use alternative sets of assumptions for a deterministic model.
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15
Q

Scenario analysis

A

The likely impact of a CATASTROPHIC EVENT on a firm’s outstanding liabilities is measured.

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16
Q

Scenario analysis:
3 ways of deriving a scenario

A
  • basing it on an historical event
  • thinking up a hypothetical event using our judgement, or
  • from the results of a stochastic model
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17
Q

Scenario analysis:
8 Typical scenarios affecting outstanding liabilities

A
  • claims outstanding from single catastrophes
  • claims outstanding on major individual contracts
  • latent claims
  • reinsurance bad debt
  • interest rate changes
  • inflation levels affecting the ultimate size of claims paid
  • expense levels
  • exchange rate movements if claims are paid in foreign currency.
18
Q

6 Main advantages of scenario testing

A
  • Provides an advantage over a stochastic model by allowing a more detailed analysis of the TAIL end of the reserve distribution.
  • In performing a scenario test, we pay particular attention to the likely coincidence of these adverse factors.
  • A scenario analysis is more FOCUSED.
  • We can construct a scenario test and produce reliable results much more QUICKLY than for a stochastic model (since it is aimed at the specific question)
  • It is easier to COMMUNICATE the results of scenario tests than the results of stochastic models, as they are more transparent.
  • Model uncertainty is much less of a problem when we construct scenario tests because we consider the driving factors explicitly.
19
Q

3 Main disadvantages of scenario testing

A
  • No specific probability associated with the outcomes and so it is not possible to construct a distribution of outcomes.
  • Scenarios typically only give information on the extremes of the distribution of eventual outcomes, while the actuary may want to disclose information on the overall distribution to stakeholders too.
  • The method is more subjective than the other methods, since the actuary makes the decisions on which extreme scenarios are to be investigated.
20
Q

3 relative merits of stochastic and deterministic approaches

A
  • Deterministic approaches only consider a limited number of factors and one result from each, while a stochastic model generates a number of potential scenarios that may not be thought of under a deterministic approach.
  • Failure is often due to the interaction of many differing factors which could not be modelled deterministically. The stochastic model can allow for the interdependency of these key factors.
  • Analysis of the impact of atypical scenarios aids understanding of variation around expected outcomes, and assigns a distinct value to them.
21
Q

7 Uses of stochastic reserving

A
  • To assess reserve adequacy in absolute and relative terms.
  • Compare the reasonableness of different sets of reserve estimates.
  • Compare datasets at different as at dates.
  • Monitor performance to see if claims movements are material.
  • Allocate capital.
  • Provide information to investors.
  • Inform discussions with regulators.
22
Q

Define “reserve risk”

A

The risk in respect of financial losses that could arise if the actual claim payments from expired business turn out to be higher than reserved for.

23
Q

3 Main benefits of using a stochastic approach for reserving

A
  • We can estimate the reliability of the fitted model, and likely the magnitude of random variation
  • We may apply statistical tests to the modelling process to verify any assumptions and gain understanding of the variability of the claims process.
  • We can develop models in which the influence of each data point in determining the fitted model depends on the amount of random variation within that data point.
24
Q

4 Components of model error

A
  • specification error
  • selection (“systemic”) error
  • Estimation or parameter error
  • Process error
25
Q

Estimation or parameter error

A

Arises from the fact that the estimated parameters are random variables.

26
Q

Selection (“systemic”) error

A

Arises from incorrect selection of the underlying data used.

27
Q

Specification error

A

Arises from the specification of the model.

28
Q

3 ways in which the appropriateness of any model might be tested

A
  • Examine plots or triangles of residuals
  • Use F tests to check the appropriateness of the number of parameters.
  • Fit the model to past data
29
Q

Analytical methods:
3 Distributions which might be specified for the claims process:

A
  • over-dispersed Poisson
  • negative binomial
  • normal approximation to negative binomial
30
Q

Mack model

A

The Mack model reproduces chain ladder estimates, and make limited assumptions about the distribution of the underlying data, specifying the first two moments only.

31
Q

3 Key assumptions of the Mack model

A
  • the run-off pattern is the same for each period
  • the future development of a cohort is independent of historical factors
  • the variance of the cumulative claims to development time t is proportional to the cumulative claims amount to time t-1.
32
Q

Bootstrapping

A

Involves sampling (with replacement) multiple times from an observed data set in order to create a number of pseudo data sets.
We can then refit the model to each new data set, and obtain a distribution of the parameters.

In the context of claims reserving, “bootstrapping” often refers to bootstrapping the ODP (over-dispersed Poisson) model.

33
Q

4 Keys assumptions of “Bootstrapping/ODP model”

A
  • the run-off pattern is the same for each origin period
  • incremental claim amounts are statistically independent
  • the variance of the incremental claim amounts is proportional to the mean
  • incremental claims are positive for all development periods.
34
Q

Why might claims run-off between lines of business be correlated? (3)

A
  • reporting delays may change across all classes,
  • the same claims team may handle claims from several lines and so changes to claims handling may impact on more than one line
  • of problems with data that affect more than one line of business.
35
Q

3 Types of stochastic claims reserving models

A
  • analytical methods
  • simulation methods
  • Bayesian methods
36
Q

5 Issues with stochastic claims reserving models

A
  • Claims need to be aggregated across lines of business. This process needs to allow for correlations.
  • Certain models are limited by the type of model or data that can be fitted. A key problem is with instances of negative increments in incurred data.
  • Stochastic models can be unreliable when applied to latent claims.
  • Models fitted using sparse data can be very sensitive to small changes.
  • Care is required in the tail of the claims distribution because data may be inadequate and assumptions may not be valid at the extremes.
37
Q

Bayesian stochastic reserving method

A

Bayesian methods use
… a prior distribution for the variable
… in combination with the data
… to produce a posterior distribution for the predicted variable

38
Q

3 Advantages of the Bayesian method

A
  • they provide a complete predictive distribution
  • they explicitly state the subjective judgement used
  • closed-form distributions can often be obtaines
39
Q

2 Disadvantages of the Bayesian method

A
  • the choice of prior distribution is subjective
  • numerical methods are required when there is no closed-form distribution
40
Q

3 Methods to use in the absence of any past claims data

A
  • Using market data or data from reinsurers
  • Applying a percentage to the policy limit
  • using professional judgement and experience
41
Q

7 Objectives in communicating uncertainty

A
  • ensuring stakeholders UNDERSTAND the level of uncertainty
  • being CONSISTENT with the vocabulary used by other actuaries and explaining any terms
  • emphasising the bigger issues
  • explaining what has been allowed for in the best estimate, and what has not
  • emphasising the unusual issues
  • commenting in the context of the scope and purpose
  • avoiding misunderstandings
42
Q

5 Drawbacks to stochastic reserving

A
  • It takes more time
  • It requires a higher level of skill and training
  • The methods are more complicated, so the risk of mistakes is greater and they are harder to explain to a non-technical audience
  • A considerable element of judgement is required in the choice of model and in selecting a prior (Bayesian methods)
  • Using more sophisticated methods may lead to spurious accuracy and false confidence in the results.