Hi, I'm going through the solution for this part and am slightly confused as to the reasoning behind the linear interpolation for the 2009 year being= 0.75*claims paid in dev (x) +0.25* claims paid in dev (x+1). I understand that because the policies are first written on 1 July, we need to adjust these numbers but I'm struggling to get the rationale behind the above formula. Thanks.
For the 2009 underwriting year, assuming policies incept uniformly over the calendar year, the average inception date is 1 October 2009. The business will therefore be 0.25 years developed on average by the end of the underwriting year, 1.25 years developed on average by the end of the next year etc. For the 2010-2013 underwriting years, assuming policies incept uniformly over the calendar year, the average inception date is 1 July each year. The business will therefore be 0.5 years developed on average by the end of the underwriting year, 1.5 years developed on average by the end of the next year etc. Therefore to adjust the 2009 underwriting year to be at the same stage of development as the later years at each point in time, you need 75% of the first figure and 25% of the second one.
