Solve these Microeconomics questions

7 The general form of a run-off triangle can be expressed as: Accident Development Year, j Year, i 0 1 2 3 4 5 0 Co.D C1,0 62,0 63,0 C4,0 C5,0 1 Co.1 C11 C2,1 63,1 C41 2 Co.2 C1,2 C2,2 C3,2 3 Co.3 C13 C2,3 4 Co.4 C1,4 5 Co,5 Define a model for each incremental entry, Cy, in general terms and explain each element of the formula. [4] 8 Claims arrive in a Poisson process at rate / . Individual claim amounts are all exactly 100. The insurer applies a premium loading factor of 20%. (i) (a) Show that the adjustment coefficient, R , satisfies: 100R -1208-1=0 (b) By approximationg edwith a series expansion up to terms in R", obtain an approximate value of R . [4] (ii) Determine the minimum initial capital such that the probability of ruin is at most 0.05. [2] [Total 6] 9 The table below shows the payments made in each development year in respect of an insurer's claims for fire damage for the three most recent calendar years. You may assume that all claims are paid in the middle of each year. Claim payments made Development year during year (f'000) 0 1 2 2010 830 940 150 Accident 2011 850 year 2012 1,120The rate of claims inflation over these years, measured over the 12 months to the middle of each year are given below: Annual claim inflation rate Estimated annual claim (past) inflation rate (future) -2011 2% -2013 3% -2012 2.5% -2014 3% Use the inflation adjusted chain ladder method to estimate the total amount outstanding for future claims arising from accident years 2011 and 2012. [8] 10 Cumulative claims incurred on a motor insurance account are as follows: Cumulative claims Development year incurred (f'000) 0 1 2 2010 1,417 1,923 2,101 Policy year 2011 1,701 2,140 2012 1,582 The data have already been adjusted for inflation. Annual premiums written in 2012 were f3,073,000 and the ultimate loss ratio has been estimated as 92%. Claims paid to date for policy year 2012 are f441,000, and claims are assumed to be fully run-off by the end of Development year 2. Estimate the outstanding claims to be paid arising from policies written in 2012 only, using the Bornhuetter-Ferguson technique. [6]