Actuarial Science

Actuarial Science SPRING 2016 ACTUARIAL METHOD I PROF. RAMANUJAM Homework Set #2 1. You are given: i) qx = 0.2 ii) qx+1 = 0.4 iii) qx+2 = 0.6 iv) qx+3 = 0.8 v) qx+4 = 1.0 vi) ?? = 0.06 Calculate a) Ax; b) ????:3¯| 1 ; c) ????:3¯| 1 ; d)2Ax 2. You are given: i) qx = 0.2 ii) 1|???? = 0.2 iii) 2|???? = 3|???? = 4|???? = 0.2 i) ?? = 0.06 Calculate a) Ax; b) ????:3¯| 1 ; c) ????:3¯| 1 ; d)2Ax 3. In problem #1, calculate ??¯?? and 2??¯?? under UDD 4. In problem #2, calculate ??¯ ??:3¯| and 2??¯?? under UDD 5. You are given: i) ??50:¯2¯¯0¯¯| = 0.42247 ii) ??50:¯2¯¯0¯¯| 1 = 0.14996 iii) ??50 = 0.31266 Calculate ??70 6. You are given: i) ???? = 0.25 ii) ????+20 = 0.4 iii) ????:¯2¯¯0¯¯| = 0.55 iv) ?? = 0.03 Calculate 10000 ??¯ ??:¯2¯¯0¯¯| under a) UDD and b) claims acceleration method 7. You are given: i) (IA)50 = 4.99675 ii) ??50:1¯| 1 = 0.00558 iii) ??51 = 0.24905 iv) ?? = 0.06 Calculate (IA)51 8. You are given: i) X denotes the present value of the random variable for n-year endowment and Y denotes the present value of the random variable for n-year term insurance(X and Y are both continuous). ii) Var(X) = 0.0052 iii) vn = 0.3 iv) npx = 0.8 v) E(Y) = 0.04 Calculate Var(Y) 9. ??1 = { ?????? , ???? = ?? 0, ???? > ?? and ??2 = { 0, ???? = ?? ????, ???? > ?? Calculate Cov(Z1, Z2) 10. You are given: x lx Ax 35 100000.00 0.151375 36 99737.15 0.158245 37 99455.91 0.165386 38 99154.72 0.172804 39 98831.91 0.180505 40 98485.68 0.188492 ?? = 6% Calculate a) 5E35; b) ??35:5¯| 1 ; c) 5|??35; d) ??¯ 35:5¯| under UDD