In my opinion, the exam was balanced in terms of its difficulty, nevertheless, it was difficult as compared to the last three sessions. Major issue was that of time management.
Q No 1 : This question was related to autoregressive time seires and comprised following two parts: (a) Express the time series in terms of white noise process (2) (b) Calculate the variance (2)
Q No 2 : Losses corresponding to four decision functions were given in relation to different nature decisions. (a) Can any of the decision functions be discarded? (1) (b) What is the minimax solution? (2) (c) What is the solution under Baye's criterion? (2)
Q No 3 : An exponential aggregate loss function was given. It was required to calculate the probability of NO ruin by the end of 2nd year. Annual premium was 15 and the mean of the exponential distribution was 10. (5)
Q No 5 : 8 values from a lognormal distribution were given. (a) Calcuate mean and variance by using method of moments (5) (b) Calculate mean and variance by using lower and upper quartiles (5)
Q No 6 : Cumulative claims were given and reserve was required to be calculated by using: (a) Chain Ladder Method (6) (b) Bornhueter Ferguson Method (6)
Q No 7 : Experience rating question (a) Write down the transition matrix (4) (b) Calculate the steady state equilibrium proprtions of policyholders at different discount levels and express them in terms of "k" (4) (c) Calculate the average premium of high risk category policyholders (2) (d) Comment on the difference in the avg premiums (2)
Q No 8 : This was a time series question and various sample values were given. (a) Calculate the values of a1, meu and sigma (7) (b) Apply turning points test (3)
Q No 9 : A binomial distribution was given as a likelihood function and beta distribution was the prior one. (a) What is conjugate prior? (1) (b) Derive the posterior distribution (3) (c) What is expected value of (1/X) (4) (d) What is the value of d* (3) (e) Express D# in terms of Z and !-Z (2) (f) Comment on the difference in the values (2)
Q No 10 : Compound poisson distribution was given (a) Derive the moment generating function of the aggregate claim amount (4) (b) Derive the mean and variance (6) (c) An insurer was supposed to bear the claim amounts that followed an exponential distribution. If the individual claim amount exceeded 200, the insurer was supposed to pay an additional amount of 50 for every claim. Calculate the mean and variance of aggregate claim amount. (9)
Q No 4 : It was a GLM question. (a) Calulate the MLE of theta(ij) (3) (b) Express it in terms of exponential family (2) (c) A predictor function was given as alpha + Beta * X and it was required to recommend any other suitable function. (3)
I think, in this question we can calculate the probability either by assuming the normal approximation or directly calculating the integral of exponential function.
I think in the calculation of reserve, we had to include the total value of incurred claims because neither it was stated that the claims have been paid nor any paid value was given.
I used the normal approximation.. Could anybody else confirm which approach is correct/appropriate..??
Yes I agree with evergreen that neither it was stated that the claims have been paid nor any paid value was given so there seem to be some confusion here..
I agree with evergreen.. The exam was a bit more difficult in comparison to last three sittings.. Proving the time series identity (Q1), writing the linear predictor (Q4), Calculating the mean & variance through percentile method (Q5), Proving E(1/X) (Q6), Stating in the form of credibility form (Q6), Calculating the given time series data (Q7), Proving the equilibrium states in terms of k (Q8) are the major things which made this exam more difficult in comparison to last three sessions..
