Chapter 5: Life Annuity
5.2 Continuous Life Annuity
Here we assume the payment is a unit benefit of $1 per year.
Chapter 5: Life Annuity
In general: the APV for a continuous annuity is:
0
v t P[paymen
Chapter 4: Life Insurance
4.1 Insurance Payable at the Moment of Death
Lets consider insurances that are payable at the moment of
Chapter 4: Life Insurance
affects when and whether the benefit is paid
Stat 353 Practice Midterm Exam
Stat 353 Practice Midterm Exam
1) The survival function S(x) = e -x/100 for x > 0. Find the
k) a(20),
instantaneous death rate (x). If K(x) is the curtate further
lifeti
Stat 353 Practice Problem Set #1
20000 100 x x 2
for x 0
20000
Find w (the oldest age that a life can live)
Calculate the probability of surviving to age 20.
Calculate the probability that a life aged
Chapter 3: Survival Distributions and Life Tables
3.1 Survival Function
Chapter 3: Survival Distributions and Life Tables
Survival Function:
Let s(x) be a survival function of X:
Let X be the age-at
Stat 353 Winter 2018 Quiz #1 Solution
Name: _
Student ID: _
You are allowed to use notes and a non-programmable calculator. All decimal places
should be use for intermediate steps. Please circle your
Stat 353 Problem Set 3 Solution
1. A life annuity immediate paying $1 per year to (97) until his death where i = 0.02 and
x
97
98
99
100
lx
100
71
37
0
Let Y be the present value of the payments. Find
Stat 353 Problem Set 4 Solution
1. The pricing actuary at Company XYZ sets the premium for a fully continuous whole
life insurance of 1000 on (80) using the equivalence principle and following assumpt
Stat 353 Problem Set 2 Solution
1) You are given that
a) Deaths follow the constant force assumption over each year of age,
b) qx = 0.06,
c) qx+1 = 0.07,
d) A1 = 0.054
x:1
2
Find A1 .
x:2
2) Assume th
Stat 353 Problem Set 2
1) You are given that
a) Deaths follow the constant force assumption over each year of age,
b) qx = 0.06,
c) qx+1 = 0.07,
d) A1 = 0.054
x:1
Find 2 A1 .
x:2
2) Assume that the mo
Chapter 7: Benefit Reserves
Fully Continuous Benefit Reserves
A whole life policy on a fully continuous basis with an
annual continuous benefit premium rate of P (Ax ) .
t
L = vT ( x ) t P ( Ax )aT (
Chapter 6: Benefit Premiums
6.1
Introduction to Benefit Premiums
Equivalent principle:
E [L ] = E [PV of Benefits ] E [PV of Premiums ] = 0
Fully Continuous Premiums
whole life insurance
L = 1 v T P a
Chapter 5: Life Annuity Summary
Continuous Life Annuity
Cumulative Distribution of Y
1 e T
ln(1 y )
FY ( y ) = P[Y y ] = P
y = FT
Density Function of Y
1 ln(1 y )
fY ( y ) =
fT
1 y
0< y<
Stat 353 Fall 2006
Assignment 2 Solution
Due: Friday, October 20, 2006 by 3pm
1) You are given that
a) Deaths follow the constant force assumption over each year of age,
b) qx = 0.06,
c) qx+1 = 0.07,
Stat 353 Fall 2006
Assignment 1 Solution
Due: Friday, October 6, 2006 by 3pm
20000 100 x x 2
for x 0
20000
a) Find w (the oldest age that a life can live)
20000 100 w w 2
= 0 w = 200 or
Since s ( w) =
Chapter 4: Life Insurance Formula Summary
Continuous Insurance
n-year term life insurance
Ax : n | = E[Z ] = vt t px ( x + t )dt
E[ Z 2 ] = v2 t t p x ( x + t ) dt = Ax : n |
n
1
n
0
2
2
1
0
( )
Var[Z
Stat 353 Practice Problems #1 Solution
20000 100 x x 2
for x 0
20000
a) Find w (the oldest age that a life can live)
20000 100 w w 2
Since s ( w) = 0, we have s ( w) =
= 0 w = 200 or
20000
Therefore,