Chapter 15: Quantifying uncertainty in reserves

Question 1

9 Random factors influencing the run-off of claims reserves

Answer 1

• 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

Question 2

“Heads of damage”

Answer 2

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

Question 3

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

Answer 3

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

Question 4

4 Terms used to identify the sources of uncertainty

Answer 4

• Parameter uncertainty
• Process uncertainty
• Model error
• Systemic error

Question 5

Process uncertainty

Answer 5

The uncertainty in what the future outcome will be.

This is the randomness of the underlying process.

Question 6

Parameter uncertainty

Answer 6

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

Question 7

Model error

Answer 7

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

Question 8

Systemic error

Answer 8

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

Question 9

3 Types of ranges that might be used

Answer 9

• range of best estimates
• range of possible outcomes
• range of reasonable / probable / plausible outcomes

Question 10

“Range of possible outcomes”

Answer 10

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.

Question 11

“Range of reasonable / probable / plausible outcomes”

Answer 11

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.

Question 12

Stochastic claims reserving can be used to: (6)

Answer 12

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

Question 13

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

Answer 13

• 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.

Question 14

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

Answer 14

• 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.

Question 15

Scenario analysis

Answer 15

The likely impact of a catastrophic event on a firm’s outstanding liabilities is measured.

Question 16

Scenario analysis:

3 ways of deriving a scenario

Answer 16

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

Question 17

Scenario analysis:

8 Typical scenarios affecting outstanding liabilities

Answer 17

• 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.

Question 18

6 Main advantages of scenario testing

Answer 18

• 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.

Question 19

3 Main disadvantages of scenario testing

Answer 19

• 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.

Question 20

3 relative merits of stochastic and deterministic approaches

Answer 20

• 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.

Question 21

7 Uses of stochastic reserving

Answer 21

• 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.

Question 22

Define “reserve risk”

Answer 22

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.

Question 23

3 Main benefits of using a stochastic approach for reserving

Answer 23

• 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.

Question 24

4 Components of model error

Answer 24

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

Question 25

Estimation or parameter error

Answer 25

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

Question 26

Selection (“systemic”) error

Answer 26

Arises from incorrect selection of the underlying data used.

Question 27

Specification error

Answer 27

Arises from the specification of the model.

Question 28

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

Answer 28

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

Question 29

Analytical methods:

3 Distributions which might be specified for the claims process:

Answer 29

• over-dispersed Poisson
• negative binomial
• normal approximation to negative binomial

Question 30

Mack model

Answer 30

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

Question 31

3 Key assumptions of the Mack model

Answer 31

• 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.

Question 32

Bootstrapping

Answer 32

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.

Question 33

4 Keys assumptions of “Bootstrapping/ODP model”

Answer 33

• 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.

Question 34

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

Answer 34

• 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.

Question 35

3 Types of stochastic claims reserving models

Answer 35

• analytical methods
• simulation methods
• Bayesian methods

Question 36

5 Issues with stochastic claims reserving models

Answer 36

• 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.

Question 37

Bayesian stochastic reserving method

Answer 37

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

Question 38

3 Advantages of the Bayesian method

Answer 38

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

Question 39

2 Disadvantages of the Bayesian method

Answer 39

• the choice of prior distribution is subjective

- numerical methods are required when there is no closed-form distribution

Question 40

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

Answer 40

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

Question 41

7 Objectives in communicating uncertainty

Answer 41

• 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

Question 42

5 Drawbacks to stochastic reserving

Answer 42

• 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.