Couret.Venter

Reading: Couret, J. and Venter, G., "Using Multi-Dimensional Credibility to Estimate Class Frequency Vectors in Workers Compensation"

Synopsis: To follow...

Study Tips

Still to come...

Read this after Robertson.HazardGroups

Estimated study time: 3 hours (not including subsequent review time)

BattleTable

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

• fact A...
• fact B...

reference	part (a)	part (b)	part (c)	part (d)
E (2018.Spring #1)
E (2018.Spring #1)
E (2018.Spring #1)
E (2018.Spring #1)
E (2018.Spring #1)
E (2018.Spring #1)
E (2018.Spring #1)
E (2018.Spring #1)

In Plain English!

Claim counts for workers compensation classes are unreliable for serious injuries because of the low frequencies involved. However, serious injury types are correlated with other injuries as the situations which cause fatal (F), permanent total (PT), and major permanent partial (Major) injuries are usually similar. It is generally only a small difference in the situation that results in a significantly different outcome. So a class with a lot of major injuries probably has a higher than average likelihood for permanent total and fatal injuries.

Couret and Venter derive a multivariate correlated credibility by estimating the population mean for each injury type by class using a linear function of the sample means for all of the injury types in the class. The coefficients of the linear function are estimated by minimizing the expected squared error.

They apply this method to ratios of claim counts by injury type to temporary total impairment (TT) claim counts. That is, they treat a temporary total injury as an exposure which could have produced a higher severity claim (F, PT, Major, or Minor). Let V, W, X, and Y be the observed ratios for injury types F, PT, Major, and Minor. The paper assumes the distribution of clami counts by injury type is parametrizable for each class but the parameters are unknown. Let v_i, w_i, x_i, and y_i be the population (hypothetical) mean ratios. Then the observed sample claim count ratio of permanent total (PT) to temporary total (TT) for class i at time t is given by [math]M_{i,t}*W_{i,t}=\sum_{j=1}^{m_{i,t}}w_i+\epsilon_{i,t}[/math]. Here, there are [math]m_{i,t}[/math] TT claims, and the [math]\epsilon_{i,t}[/math] are independent perturbations with mean zero and standard deviation [math]\sigma_{W_i}[/math] which vary by class but not time. Hence each TT claim is considered an exposure which may or may not produce a PT claim.

Rearranging the equation gives [math]W_{i,t}=w_i+\sum_{j=1}^{m_{i,t}}\frac{\epsilon_{i,t}}{m_{i,t}}[/math] and [math]Var(W_{i,t}\;|\; w_{i,t})=\frac{\sigma^2_{W_i}}{m_{i,t}}[/math]. Hence, the more TT claims, the smaller the random fluctuations of the annual observed class ratio [math]W_{i,t}[/math] from its population mean.

A key assumption of Couret and Venter's analysis is the variance of F, PT, Major and Minor claims decreases as the number of TT claims increases. That is, the more TT claims you have, the more of the other claim types you should have and hence their variance should decrease.

Let W_i be the sample class mean ratio over all time. Assume there are N independent time periods. Then [math]W_i=\frac{\sum_{t=1}^N m_{i,t}W_{i,t}}{\sum_{t=1}^N m_{i,t}}[/math].

Let m_i be the sum of [math]m_{i,t}[/math] over all time, and m be the sum over all classes i of m_i. Then [math]Var(W_i \;|\; w_i)=\frac{\sigma^2_{W_i}}{m_i}[/math].

The same calculations are also performed for each of the 7 hazard groups discussed in Robertson.HazardGroups. These will become complements of credibility.