- Claim sizes and frequencies are generally modelled using Gamma and Poisson distributions respectively.
- Otherwise, there would need to be further examination of the response variable.
2-Pick link function
- This depends on the nature of the response variable. For example, a non-negative variable would use the log link function, whereas a variable between 0 and 1 would use a logit link function.
- What explanatory variables have been provided?
- What does the response variable look like by each explanatory variable? One way summaries or pivot tables could be analysed for insight.
- Consider grouping for categorical variables.
- Consider transformations for variables with non-linear shapes.
4-Optimising/fitting using maximum likelihood estimation (most likely done with a program).
5-Assessing output and p values
- Some variables may be dropped based on their statistical insignificance.
- Data mining or decision trees can help to find areas that are not fitting well and refine them.
- Address any large individual observations or outliers distorting results.
- Fitting curves to reduce over-fitting.
- This may be an iterative process requiring judgment.
6-Testing how well the GLM predicts using a subset of the data
There are four main approaches to pricing insurance products:
– Market rate pricing
– Target pricing
– Cost-plus pricing
– Demand-adjusted pricing
Additional methods include:
– Reinsurance driven pricing
– Sound rating
Choosing the Right Model
I thought it might be a good time to write up a summary on the major considerations needed in regards to choosing the right reserving model for the purpose required.
Choice of method depends largely on a few key factors but certainly not limited to:
- estimates purpose
- nature of business (long tail vs short tail, payment pattern, motor/workers comp/public liability etc.)
- data availability
- regulatory requirements (PS300, GPS310 etc.)
- claims handling procedures (potential changes, etc.)
- case estimating procedures (potential changes, consistency etc.)
- prior valuation methods used
- time available
||When to use
||data is scarce
incurred cost is available
|may show trends in claims cost but not always able to explain
|PPCI – Payments Per Claim Incurred
||per claim rates of payment are the same for all accident year
(Short tail classes)
|Change in payment pattern may result in over or underestimating OCL (sensitive to small movements in data)
|PPCF – Payments Per Claim Finalised
||lump sum payments
(when no significant lag between settlement and finalisation)
rates of finalisation and ACS per duration are stable
|Rates of finalisation can be distorted:
– backlog of claims
– claim cleanup campaigns
– change in settlement payment levels
– ongoing legal and admin fees
should not be used for periodic payments
|PPCS – Payments Per Claim Settled
||lump sum payments
(where there are potentially ongoing legal and admin fees post settlement and finalisation is delayed)
|as per PPCF
||shorter term periodic payments
||change in claims reporting or finalisation rate over time
||Forces claims to a fixed rate of finalisation
Does not allow order in which claims are finalised to change
|PCE – Projected Case Estimates
||small number of claims
(used for runoff portfolio, older accident years – the tail, etc.)
|reliable, stable, consistent claim estimating processes (claim estimates may be wrong but as long as they are consistent the PCE method can still be used)
|Bornhuetter-Ferguson – Loss Ratio Method
||portfolio with limited or volatile experience or inadequate size / incurred claim development is lumpy
(e.g reinsurance portfolios, new products, small liability portfolios etc.)
|selecting loss ratios (as per pricing assumptions or industry experience)
change in level of pricing (would affect selected loss ratio)
|Annuity Method / PPCOB
||longer term periodic payments (eg long term disablement payments)
||can be done at an aggregate or claim level
data must be available to develop a continuance table (may need disability and sickness tables or decrement rates if experience limited)
analysis of average weekly earnings needed
assumptions for rate of recovery
It is not always the case that one model must be selected, multiple models can be fitted and blended together to arrive at an acceptable OCL. Generally speaking a common approach to blending models together is to use BF method to model the latest years, a PPCI/PPCF approach for middle years, and the PCE method for the older years. Another reason for using a blended approach is when there is a significant departure from historical experience between accident years.
Internal capital models provide a way for an entity to analyse and assess it’s inherent risks and formulate the required capital to sustain the entity and meet objectives. The key user of these models is generally the board who use it to decide how much capital the firm should hold. Other divisions can also make use of outputs from the model to fulfil their requirements.
In general insurance they are used in a number of applications:
- First and foremost they aid the insurer in setting the amount of capital held.
- They enhance the understanding of risk and provide an input into the risk management framework.
- They can be used to help set the Reinsurance programme.
- They can help business make key decisions.
They provide two key outputs:
- Required Regulatory Capital
- Economic capital
Required Regulatory Capital is the amount of capital the regulator requires insurers to hold. In Australia APRA requires insurers to maintain capital above the Prescribed Capital Amount (PCA). Insurers tend to hold what is often termed as Economic capital. This is the amount of capital the insurer will hold to meet it’s objectives. (e.g. RORBC, ROE, etc.) This is greater than the required regulatory capital.
Internal capital models model the following risks:
- Insurance Risk
- Credit Risk
- Asset Risk
- Operational Risk
- Interest Rate Risk
Dependancy structures are also modelled.
Insurance is one of those industries that tend to be heavily constrained by regulation in most jurisdictions. Certain classes such as CTP and Workers Compensation tend to have more than others. The four key areas that are impacted by regulations include:
- Product coverage
- Premium setting
- Licensing requirements
Insurance market deregulation can result in a lot of benefits to the market as a whole. Although as with any major change there are going to be negative effects as well. I’ve listed a few of these below from the view points of the consumer and the insurer.
||– More product choices
– Risk based pricing
– Increased access to insurance
– Lower premium due to less legal requirements for Insurer
|– Ability to compete on product offering
– Differentiate risks
– More avenues of distribution
– Lower requirements – reducing capital/compliance costs
||– Products harder to compare
– Less cross subsidization
– Insurers may pass on distribution costs
– Higher insolvency risk
|– Cost of product development
– Cost of pricing and technology
– Cost of distribution
– Increased competition
The common regulated pricing structures include:
– Reference Premium Rates
– Elastic caps and floors
– Restrictions on rating variables
– Fixed loading structure
Reinsurance is basically insurance for insurers.
There are broadly speaking two classes of reinsurance:
- Proportional: Reinsurer covers a risk by taking a cut of the premium and covering any losses in proportion to the amount of risk ceded
- Non-proportional: Reinsurer covers losses in excess of a certain amount for a premium
Proportional reinsurance includes:
- Quota share reinsurance
- % of risk ceded to the reinsurer
- insurer and reinsuer share premiums and losses as they arise on an equal proportion
- Surplus reinsurance
- offers coverage to larger risks above a certain threshold and up to a certain limit of Sum Insured
- the cost sharing of losses is on a proportional basis as follows
Non-proportional reinsurance includes:
- Excess of Loss reinsurance
- reimburses losses above a certain limit to the insurer
- sold on a per risk basis or on an event basis