The following table records all claims that occurred from 1 April 2010 and were reported by 31 October 2013.

Loss ID Occurred Reported Delay (days) Delay (years)

R01 29/7/2011 21/12/2012 511 1.399 R02 14/2/2013 10/3/2013 24 0.066 R03 17/7/2011 22/1/2012 189 0.517 Loss ID Occurred Reported Delay (days) Delay (years)
R04 8/6/2011 5/2/2013 608 1.665 R05 3/8/2011 15/3/2012 225 0.616 R06 13/9/2011 10/10/2011 27 0.074 R07 21/7/2011 10/10/2013 812 2.223 R08 3/11/2011 8/6/2013 583 1.596 R09 15/9/2010 27/7/2011 315 0.862 R10 10/9/2010 17/6/2011 280 0.767 R11 7/11/2011 12/4/2012 157 0.430 R12 10/1/2011 19/3/2011 68 0.186 R13 2/8/2011 19/1/2013 536 1.467 R14 28/7/2010 27/4/2011 273 0.747 R15 11/6/2010 12/7/2011 396 1.084 R16 7/3/2013 20/7/2013 135 0.370 R17 29/11/2010 10/3/2011 101 0.277 R18 13/7/2012 18/9/2013 432 1.183 R19 17/6/2010 17/8/2013 1157 3.168 R20 18/4/2010 16/7/2010 89 0.244 Average 337 0.923 Assuming that the policy year is from the 1 April to 31 March and that the delays between occurrence and reporting follows an exponential distribution:

a. Estimate the mean delay between occurrence date and reporting date.

b. Estimate the number of IBNR claims for the period 1 April 2010 to 31 October 2013 using the triangle-free method.

c. Build a development triangle based on the loss data with an appropriate observation period and estimate the number of IBNR claims for the period 1 April 2010 to 31 October 2013 using the triangle development method (you can choose the calendar year for ‘bucketing’).

d. Comment on the relative advantages of the triangle-based and triangle-free IBNR calculation methods in general and as they manifested themselves in the example above.
State explicitly all assumptions that you used throughout the exercise.