As per your request here I am sharing the previous year question paper of Annamalai University for PG Diploma in Actuarial Science-Advanced Topics in Actuarial Statistics Exam

SECTION-A

Answer FIVE questions (58=40)

1. Explain the meaning of fully continuous premiums.

2. What is meant by exponential premium? State its essential features.

3. Explain in detail paid-up insurance.

4. Write a note on benefits reserve on a semi-continuous basis.

5. Interpret the following differential equation:

6. Distinguish between discrete insurance and continuous insurance

7. Mention the importance of Lexis diagram

8. Interms of single life probabilities npx and npy, express the probability that both lives will die within n years.

SECTION-B

Answer any THREE questions (320=60)

9. a) Define approtionable premiums. Derive the formula for fully discrete benefit reserves.

(OR)

b) Find the 25th percentile premium for an insured age 55 for the following plan of insurance: (i) 20 year term (ii) 10 year term.

10. a) What do you understand by retrospective formula? Derive the same.

(OR)

b) Obtain the expression for benefit reserves based on true monthly benefit premiums.

11. a) Explain the procedure involved in the computation of semi-annual premiums with claims paid at the end of the insurance year of death.

(OR)

b) Examine in detail benefit reserves at fractional durations.

12. a) Obtain the distribution of time-until –failure of a joint life status.

(OR)

b) For two lines (x) and (y) the joint p.d.f. of their future life times, T(x) and T(y) is .

Determine the following:

(i) The joint density function of T(x) and T(y)

(ii) The correlation coefficient of T(x) and T(y)

13. a) Write an explanatory note on Lexis diagram.

(OR)

b) Explain the following in detail.

(i) Stationary population

(ii) Stable population

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