Fisher.ExpRating

Reading: Fisher, G., et al., "Individual Risk Rating Study Note" CAS Study Note Version 3 October 2019, Chapter 1

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Based on past exams, the main things you need to know (in rough order of importance) are:

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reference	part (a)	part (b)	part (c)	part (d)
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In Plain English!

Overview

Experience rating is the use of an insured's past loss experience to determine rates for a future exposure period. An experience rating plan is the set of rules, definitions, formulas, etc. which are needed to calculate such a rate. The experience rating plan generally produces a multiplicative factor called the experience modification or e-mod. The experience modification factor corresponds to the individual insured and is used to adjust the manual premium which is the starting point premium for a whole class of insureds.

The standard premium is the experience modification factor multiplied by the manual premium. This technically assumes the schedule modification factor is 1.000. If there is a non-unitary schedule factor, then the prior calculation is known as the modified premium. The standard premium is then the modified premium multiplied by the schedule modification factor. The first chapter of the Fisher paper assumes the schedule modification factor equals 1.000.

A debit mod is when the experience modification satisfies: [math]\mbox{e-mod}\gt 1.0[/math]. This implies the insured's experience is worse than average for its class.

A credit mod is when the experience modification satisfies: [math]\mbox{e-mod}\lt 1.0[/math]. This implies the insured's experience is better than average for its class.

The experience modification facilitates a comparison of the insured's expected loss relative to other risks in its class. Experience rating quantifies how much an insured's past loss experience is predictive of its future loss experience and uses this to rate prospectively with greater accuracy.

Question:

What are some advantages of experience rating?

Solution

• Account for differences between risks within a class, such as

• Different locations and equipment
• Management styles
• Use of materials
• Safety processes and level of training.

• Account for differences due to variables which are difficult, impractical, or impossible to measure using rating variables.
• Additional refinement - more useful when there are few rating classes or classes have a broad range.

Experience rating is useful because not all risks fit neatly into a class. A risk may have unique operations, or the rating system may lack sufficient refinement to group appropriately. In fact, if the rating classification plan is highly refined so there is limited variation between risks within a class then experience rating is not very useful.

Question:

What are the goals of experience rating?

Solution

• Greater risk equity: Increase fairness by charging rates that better match the expected loss(es) of the insured.
  • The size of the charge based on historical losses must reflect the extent it impacts future losses rather than attempting to recoup prior losses.
• Create an incentive for safety by placing a cost on losses. This adds a reason to prevent or minimize losses.
• Improve market competition: By better matching rate to risk, insurers should be encouraged to insure more risks as they can charge a more appropriate premium.

Gary Venter in his article "Experience Rating – Equity and Predictive Accuracy" says "... to the extent that the loss experience is indicative of true differences from the classification average, it appears equitable to charge for it." The experience modification is intended to reflect future loss experience, not to penalize or reward past experience.

Credibility for Experience Rating

Experience rating treats each risk as its own risk class, so how much credibility should be given to the insured's individual experience when determining their premium?

While there are several methods for determining credibility, such as classical/limited fluctuation, Bayesian, or Bühlmann, experience rating only uses Bühlmann credibility.

Let [math]Z=\frac{E}{E+K}[/math] where K is a constant defined by the ratio [math]\frac{\mbox{Expected Process Variance}}{\mbox{Variance of Hypothetical Means}}[/math], and E is the size of the risk (level of expected losses). Process variance (EPV) is purely random and comes from the underlying stochastic process. The Variance of Hypothetical Means (VHM) is variation resulting from an individual risk being (slightly) different from the other risks in its class. The complement of credibility is the experience of the class containing the risk. The credibility assigned, Z, represents how much of the experience is due to the difference between risks within a class.

Question:

What is the aim of using credibility weighting with experience rating?

Solution:

Aim is not to penalize an individual for random risk but encourage ownership of risk which is due to differences between the risk and other risks in its class.

The experience modification factor, M, may be expressed as [math]M=\frac{ZA+(1-Z)E}{E}=\ldots =\frac{A+K}{E+K}[/math], where A is the actual loss experience for the individual, and E is the expected loss experience for the class containing the individual.

Credibility Issues:

Maximum Single Loss (MSL)	This is the amount at which individual large losses are capped at when they are included in the calculation of a risk's experience.
Minimum and Maximum Adjustments	The experience modification factor is often subject to a maximum or minimum value to make sure the rating adjustment isn't too extreme.

The loss experience of larger risks receive greater credibility than that of smaller risks. Similarly, the maximum single loss and loss adjustments also vary with the size of the risk.

The size of the risk may be measured in various ways, such as manual premium, expected loss, expected number of claims, or using an exposure base such as sales receipts for general liability.