Actuarial Mathematics 2: Assignment 1
Question Assignment 1:
(a) Show that if µ is fixed then
+
for all
=
+
, ≥ zero
(b) For a Entire Life Coverage with loss of life advantage of $5000, profit
payable on the finish of 12 months of loss of life, decide 1 given
µ = zero. 07 and = zero. 07.
(c) Take into account the next info for a given coverage :
a. δ = zero. 03
b. Stage premium = $3500
c. No bills.
d. µ = zero. 0007
e. Profit fee = $150, 000
(i) Utilizing Thiele’s Differential Equation, resolve analytically (utilizing
calculus) for the coverage worth .
(ii) Discover the distinctive answer to this differential equation clearly
exhibiting why that is the case.
(iii) Describe the what occurs to the coverage worth as → ∞.
(d) Take into account the next coverage foundation for a 20 12 months time period life coverage
with:
Survival mannequin: De Moivre’s Legislation ω = 105
Curiosity: = zero. 06
Bills: No bills
Sum Insured: $60,000
Through the use of Microsoft Excel or in any other case, decide 10 utilizing the
numerical approximation (Euler’s Methodology) for the answer to
Thiele’s Differential Equation. Assume a time step of ℎ = zero. 05.
Complete: 20 marks
Question Assignment 2:
Take into account the next joint density perform for (2) lives (x) and (y):
( , ) = ( , ,
2
+
2
) zero < < three zero < < 2
(a) Calculate .
(b) Calculate .
(c) For an entire life coverage of a joint standing (following the mortality
mannequin above) with sum insured of $250,000, profit payable
instantly upon loss of life, decide the online single premium.
Complete: 15 marks
