Chapter 15: Quantifying uncertainty in reserves

Question 1

Uncertain factors that influence the final outcome of the run-off of claims reserves:

Answer 1

• The occurrence and severity of claims
• The notification delays on individual claims
• Legal changes that affect the size of awards
• Legal changes that affect the “heads of damage” changes in the litigiousness of society
• Levels of claims inflation
• Court rulings on liability or amount of individual claims not foreseen by claims handlers and/or not in the historic data
• Changes in the mix of claim types
• Changes in claims handling

Question 2

Terms used to identify sources of uncertainty:

Answer 2

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

Question 3

Ways of estimating the range of possible outcomes:

Answer 3

• Stochastic models
• Alternative sets of assumptions
• Scenario testing

Question 4

Reasons why the use of stochastic models may provide unreasonable results:

Answer 4

• Past data may be affected by once off events. Parameters need to be adjusted to allow for these features
• The volatility seen within the historical claims’ development may not be a good indicator of the underlying process uncertainty

Question 5

Advantages of using alternative sets of assumptions to quantify the uncertainty in reserves:

Answer 5

• Simple to use on stochastic and deterministic models
• Judgement is used when selecting possible parameters. We can therefore allow for atypical volatility in the historical data, i.e. if it is not expected to be repeated then it can be excluded from consideration

Question 6

Disadvantages of using alternative sets of assumptions to quantify the uncertainty in reserves:

Answer 6

• We assign no explicit probability to each set of parameters. It is not possible to estimate the distribution of future outcomes unless we assign a probability to each set of assumptions
• We ignore model uncertainty using this method
• We don’t allow for process uncertainty if we use alternative sets of assumptions for a deterministic model.

Question 7

Scenarios affecting outstanding liabilities:

Answer 7

• Claims outstanding from single catastrophes
• Claims outstanding on major individual contracts
• Latent claims
• Reinsurance bad debt
• Interest rate changes (if reserves are discounted)
• Inflation levels affecting the ultimate size of claims paid
• Expense levels
• Exchange rate movements if claims are paid in foreign currency

Question 8

Advantages of scenario testing to quantify the uncertainty in reserves:

Answer 8

• 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 aim a scenario test at a specific question being asked. A stochastic approach provides a full analysis which may e unnecessary = time consuming and expensive
• Because it’s aimed at a specific question, we can construct a scenario test to produce reliable results more quickly than for a stochastic model
• It’s easier to communicate the results of a scenario test 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. Stochastic models may fail to capture some of the real-life process features, especially under extreme circumstances

Question 9

Disadvantages of scenario testing to quantify the uncertainty in reserves:

Answer 9

• There is 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 since the actuary makes the decisions on which extreme scenarios to investigate

Question 10

Relative merits of stochastic and deterministic approaches of quantifying uncertainty in reserves:

Answer 10

• 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. Deterministic scenarios can be chosen in such a way as to estimate the interdependencies.
• Analysis of the impact of atypical scenarios aids understanding of variation around expected outcomes and assigns a distinct value to them. This can be done to scenarios generated by a stochastic model or scenarios generated for a deterministic model.

Question 11

Stochastic claims reserving can be used to:

Answer 11

• Assess reserve adequacy
• Compare 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 12

Main benefits of the stochastic approach to claims reserving:

Answer 12

• We can estimate the reliability of the model and likely magnitude of random variation
• We can 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 the data point

Question 13

Model error consists of:

Answer 13

• Specification error
• Selection (or systemic) error
• Estimation (or parameter) error
• Process error

Question 14

Methods of testing the appropriateness of any model we use:

Answer 14

• Examining plots or triangles of residuals
• Using F tests to establish which parameters to include
• Fitting the model to past data

Question 15

Stochastic reserving models can be broadly split into:

Answer 15

• Analytical models
• Simulation models
• Bayesian methods

Question 16

Distributions that might be specified for the claims process:

Answer 16

• Over-dispersed Poisson (ODP)
• Negative binomial
• Normal approximation to the negative binomial

Question 17

Key assumptions of the Mack model:

Answer 17

• The run-off pattern is the same for each origin period
• The future development for 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 18

Key assumptions of the Bootstrapping/ODP model:

Answer 18

• The run-off pattern is the same for each origin period
• Incremental claim amounts are statistically independent
• The variance of incremental claim amount is proportional to the mean
• Incremental claims are positive for all development factors

Question 19

Issues surrounding stochastic reserving:

Answer 19

• Claims need to be aggregated across lines of business. The 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. Data adjustments can sometimes be used in such cases
• Stochastic models can be unreliable when applied to latent claims. Exposure based methods are better here
• Models fitting using sparse data can be very sensitive to small changes. Judgement is required in these cases
• 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 20

Advantages of the Bayesian Approach to stochastic reserving:

Answer 20

• They provide a complete predictive distribution of the ultimate reserve
• It explicitly shows the impact of judgements, which is reflected in the prior distribution
• Similarly to the analytical method, it could give closed form results when an appropriate prior distribution is chosen

Question 21

Disadvantages of the Bayesian Approach to stochastic reserving:

Answer 21

• As with other Bayesian methods, the choice of prior distribution is subjective, and the posterior distribution may be over-reliant on the choice of prior distribution
• It may not give closed-form results and numerical integration may be needed to get results (Markov Chain Monte Carlo method)

Question 22

Methods that can be used to estimate reserves in the absence of any past claims data:

Answer 22

• Using market data or data from reinsurers
• Applying a percentage to the policy limit (maximum possible claim amount)
• Using professional judgement and experience

Question 23

Objectives in communicating uncertainty:

Answer 23

• Ensure stakeholder understand the level of uncertainty
• Be consistent with vocabulary used by other professionals and explain terms
• Emphasise bigger issues
• Explain what has been allowed for in the best estimate and what has not
• Emphasise the unusual issues
• Comment on the uncertainty in the context of the scope and purpose
• Avoid misunderstandings