Math 5068 (001)
Homework 2
Due 2/10/14
1. For a fully continuous 25-year 15-pay endowment insurance on (35) with face amount 1000,
you are given:
i. ,
ii.
iii.
iv.
Calculate the fifth benefit reserve .
2. For a fully continuous 20-year deferred life annui
1. For (x) you are given:
The premium for a 20-year endowment insurance of 1 is 0.0349.
The premium for a 20-year pure endowment of 1 is 0.0230.
The premium for a 20-year deferred whole life annuity-due of 1 per year is 0.2087.
All premiums are fully
Math 5068 (001)
Homework 6
Due 3/26/14
1.
(x) and (y) are independent lives. The force of mortality for each is , for 0 < t < 50. Find the joint
survival function for and : .
2. Consider two independent lives (x) and (y) where y = x + 3. If and , find the
Math 5068
Homework 1 5067 Review & Reserves
Due 1/25/17
1. The survival distribution follows a De Moivre law with = 80. The force of interest is = 0.05.
Determine the net single premium for a 5-year term insurance with benefit $1000 payable at the
moment
Math 5068
Lecture 10: Examples & Group Problem Solving
Topics:
Asset Share
Profit (gain by source)
Policy Alterations
1. For a fully discrete whole life insurance of 1000 on (x), you are given:
i.
9
AS 28.42
qx9 0.002
ii.
iii.
iv.
v.
i 0.05
The gross p
Math 5068
Lecture 8: Examples & Group Problem Solving
Topics:
Gross Reserve Recursion
Semi-Continuous Reserves
Reserve Valuation between Premium Dates
1. For a fully discrete 20-year term insurance of 100,000 on (35), you are given:
q53=.006,q 54=.007
Math 5068
Lecture 9: Examples & Group Problem Solving
Topics:
Reserve Valuation between Premium Dates (Cont.)
Thieles Differential Equation
Euler Method
1. (GPS) For a fully discrete whole life policy of 1000:
i.
The benefit reserve at fractional durat
Math 5068
Homework #8
Due 4/11
1. A homogenous discrete-time Markov model has three states representing the status of
the members of a population.
i.
State 1 = Healthy, no benefits
ii.
State 2 = Disabled, receiving Home Health Care Benefits
iii.
State 3 =
Math 5068
Homework #7
Due 3/30
1. (35) and (40) have independent future lifetimes and are subject to the mortality law
x =
1
100 x
Calculate
10
0 x < 100
q
2
35:40
2. You are pricing a special 3-year annuity-due on two independent lives, both age 80. The
Math 5068
Homework 5
Due 2/29/16
1. You are given:
i. Ax = 0.23568
ii. Ax+t = 0.28105
iii. i = 0.05
iv. Deaths are uniformly distributed between integral ages.
Calculate the semi-continuous reserve at time t for a whole life insurance on (x).
2. For a ful
Math 5068
Homework #6
Due 3/23
1. For John, currently 30 years old, the force of mortality is:
1
x =
0 x < 100
100 x
For Bob, an independent life also 30 years old it is known that
10 p30 = 0.94
5 p35 =
Math 5068
Homework 2
Due 2/1/17
1. For a fully continuous 20-year deferred life annuity of 1 issued to (35), you are given:
i. Mortality follows DeMoivres law with
.
75
ii. i = 0
iii. Premiums are payable continuously for 20 years.
Calculate the benefit
Math 5068
Homework 3
Due 2/8/17
1. You are given:
30 : 20
= 14.63
a
35 : 15
= 12.34
a
=.06
Calculate the benefit reserve at time 5 for a fully continuous 20-year endowment insurance of 1
on (30).
2. The single benefit premium for a $10,000 whole life i
Math 5068
Lecture 1: Examples & Group Problem Solving
Topics:
Introduction to Reserves
Prospective Reserve Formula
1. For a fully discrete whole life policy on (45) with face amount 1000:
i. Benefit premiums are calculated using the equivalence principl
Math 5068 (001)
Homework 3
Due 2/17/14
1. A fully discrete whole life insurance is issued to (x). You are given:
i.
ii.
iii.
Calculate i.
2. The net single premium for a $10,000 whole life insurance policy issued to (40) is $4,000. At
the end of 10 years,
1. A level premium whole life insurance of 1, payable at the end of the year of death is issued
for (x). A premium of G is due at the beginning of each year, provided (x) survives. You are
given
i. L = the insurers loss at issue when G = Px.
ii. L* = the
Math 5068 (001)
Homework 4
Due 2/24/14
1. For a fully continuous whole life insurance of 1 on (35):
i. E(L5 | T(35) > 5) = 0.05
ii. Var(L5 | T(35) > 5) = 0.23
iii. The premium is determined using the equivalence principle.
iv. 240 = 0.21
Determine the net
Math 5068 (001)
Homework 1 5067 Review & Reserves
Due 1/29/14
1. You are given
under the uniform distribution of deaths assumption.
under the constant force assumption
.
Calculate .
2. The survival distribution follows a De Moivre law with = 80. The fo
Math 5068 (001)
Homework 5
Due 3/3/14
1. For a fully continuous 5 year endowment, = 0.01 and = 0.05. Premiums are determined by
the equivalence principle. Calculate Var (L2 | T 2).
2. For a semi-continuous 20-year endowment insurance of 25,000 on (x), you
Math 5068
Spring 2014
Optional Friday Problem Solving Session: 2/14/14
1. For a special fully discrete 20-year endowment insurance on (40):
i.
The death benefit is 100 for the first 10 years and 2000 thereafter. The pure endowment benefit is
2000.
ii. The
1. For a fully discrete whole life insurance of 1000 on (60), you are given:
i.
ii. Mortality follows the Illustrative Life Table, except that there are extra mortality risks at
age 60, such that .
Calculate the annual benefit premium for this insurance.
Math 5068
Lecture 2: Examples & Group Problem Solving
Topics:
Prospective Reserve Formula
1. For a fully discrete 20-year term life insurance on (45) with face amount 1000:
i. Benefit premiums are calculated using the equivalence principle.
ii. Mortality
Math 5068
Lecture 4: Examples & Group Problem Solving
Topics:
Retrospective Reserve (cont)
Premium Relationship Formulas
Premium Difference Formulas
1. (GPS) For a special fully discrete 3-year term insurance on (x):
i. Level benefit premiums are paid
Math 5068
Lecture 3: Examples & Group Problem Solving
Topics:
Gross Premium Reserve
Expense Reserve
Retrospective Reserve Formulas
1. For a fully discrete 10-pay whole life insurance of 10,000 on (45), you are given:
i.
ii.
iii.
iv.
v.
A45 0.25
A50 0.2