Kindly solve this question well

The number of claims on a portfolio of insurance policies has a Poisson distribution with mean 200. Individual claim amounts are exponentially distributed with mean 40. The insurance company calculates premiums using a premium loading of 40% and is considering entering into one of the following re-insurance arrangements: (A) No reinsurance. (B) Individual excess of loss insurance with retention 60 with a reinsurance company that calculates premiums using a premium loading of 55%. (C) Proportional reinsurance with retention 75% with a reinsurance company that calculates premiums using a premium loading of 45%. (1) Find the insurance company's expected profit under each arrangement. [6] (Hi) Find the probability that the insurer makes a profit of less than 2000 under each of the arrangements using a normal approximation. 18] [Total 14] The table below shows cumulative claims paid on a portfolio of insurance policies. Development Year Accident Year 0 1 2 3 2007 240 281.4 302 305 2003 260 320 322 2009 270 312.9 2010 276 All claims are fully run off by the end of development year 3. (i) Calculate the total reserve for outstanding claims using the basic chain ladder technique. 171 An actuary is considering modelling the future claims assuming that individual development factors are lognormally distributed with the following parameters: Development Year Parameter 0to I 1 to 2 2 to 3 0.171251 0.035850 0.008787 0.032148 0.045606 0.046853 (ii) Show that under these assumptions the cumulative development factor to ultimate is also lognormally distributed. (iii) Calculate a 99% upper confidence limit for the outstanding claims relating to the 2010 accident year. [5] [Total 15]