Considering the case in Example 14.9.2 , what are the total estimated claims for 2008 and 2009 under the chain ladder approach? Development year (d) Earned premium 3 2 1 200 160 150 250 2007 Year of claim (c) - 200 150 300 2008 - - 200 350 2009

Each cell, [latex]X_{c,d}[/latex] , contains the number of claims that occurred in year c and were reported by the end of the d th year. To calculate an estimate for [latex]X_{2008,3}[/latex], the link ratio must be calculated using data from the claims that occurred in 2007. In particular, this link ratio, [latex]l_{2,3}[/latex] is calculated as 200/160 = 1.25. The estimated value of [latex]X_{2008,3}[/latex] is therefore 1.25×200=250. To calculate [latex]X_{2008,3}[/latex], two years’ worth of data are available, so the link ratio, [latex]l_{1,2}[/latex] is calculated as (160+200)/(150+150)=1.20. This means that the estimated value of [latex]X_{2009,2}[/latex] is 1.20×200= 240. The link ratio [latex]l_{2,3} [/latex] can then be applied to this value to estimate [latex]X_{2009,3} [/latex] is 1.25×240= 300. The claim development can therefore be completed as follows: Development year (d) Earned premium 3 2 1 200 160 150 250 2007 Year of claim (c) 250 200 150 300 2008 300 240 200 350 2009

Question 14.10: Considering the case in Example 14.9.2, what are the total e...

Financial Enterprise Risk Management

Considering the case in Example 14.9.2, what are the total estimated claims for 2008 and 2009 under the chain ladder approach?

Development year (d)			Earned premium
3	2	1	Earned premium
200	160	150	250	2007	Year of claim (c)
–	200	150	300	2008
–	–	200	350	2009

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Each cell, $X_{c,d}$ , contains the number of claims that occurred in year c and were reported by the end of the dth year. To calculate an estimate for $X_{2008,3}$ , the link ratio must be calculated using data from the claims that occurred in 2007. In particular, this link ratio, $l_{2,3}$ is calculated as 200/160 = 1.25. The estimated value of $X_{2008,3}$ is therefore 1.25×200=250.

To calculate $X_{2008,3}$ , two years’ worth of data are available, so the link ratio, $l_{1,2}$ is calculated as (160+200)/(150+150)=1.20. This means that the estimated value of $X_{2009,2}$ is 1.20×200= 240. The link ratio $l_{2,3}$ can then be applied to this value to estimate $X_{2009,3}$ is 1.25×240= 300. The claim development can therefore be completed as follows: