Fractional age assumptions for decrements
UDD in the multiple decrement table: for 0 t 1 and integer x,
0j
t px
0j
= t px
Constant transition intensities: for 0 t 1 and integer x,
0j
t px
=
Samuel Hao (University of Manitoba)
0j
px
0j (x)
00 t
00 t
1
p

7.3.4 Annual prot by source
Consider a group of identical policies issued at the same time. The
insurer makes an annual prot between t to t + 1 if:
Actual expenses are less than the expenses assumed in the policy
value basis.
Actual interest earned on inv

ACT 3230: Actuarial Models 2
Samuel Hao
University of Manitoba
Winter 2016
Samuel Hao (University of Manitoba)
ACT 3230: Actuarial Models 2
Winter 2016
1 / 16
Chapter 7: Policy Values
Assumptions:
The Standard Select Survival Model:
x = A + Bcx
with A = 0

7.3.5 Asset shares
Asset share at time t (ASt ) is obtained by accumulating to time t the
premiums received minus the claims and expenses paid in respect of a
group of policies using our estimates of the insurers actual experience
over this period and the

8.8 Multiple decrement models
A general multiple decrement model:
n R
o
00 = p00 = exp t n 0i ds ,
p
t x
t x
0 i=1 x+s
Samuel Hao (University of Manitoba)
ACT 3230: Actuarial Models 2
0i
t px
=
Rt
p00 0i ds
0 s x x+s
Winter 2016
53 / 57
The associated sin

Chapter 8: Multiple State Models
Example 1: the alive-dead model
Suppose we have a life aged x 0 at time t = 0. For each t 0 we
define a random variable Y(t) whose value is either 0 or 1.
Y(t) = 0: if the individual is alive at age x + t
Y(t) = 1: if the

8.5 Numerical evaluation of probabilities
Example 8.4 (b)
Consider the model for permanent disability illustrated in Figure 8.3 .
Suppose the transition intensities for this model are as follows
01
x = a1 + b1 expcfw_c1 x,
02
x = a2 + b2 expcfw_c2 x,
02
1

7.6 Policy alterations
After a policy has been in force for some time, the policyholder may
request a change in the terms of the policy. Typical changes might be:
The policyholder wishes to cancel the policy with immediate
effect.
CVt = cash surrender val

7.4 Policy values for policies with cash flows at 1/mthly
intervals
Example 7.10
A life aged 50 purchases a 10-year term insurance with sum insured
$500,000 payable at the end of the month of death. Level quarterly
premiums, each of amount P = $460, are p

Example 8.2
Show that, for a general multiple state model and for h > 0,
ii
h px = 1 h
n
ij
x + o(h).
j=0,j6=i
Samuel Hao (University of Manitoba)
ACT 3230: Actuarial Models 2
Winter 2016
43 / 46
8.4 Formulae for probabilities
ij
The transition intensitie

7.5 Policy values with continuous cash flows
7.5.1 Thieles differential equation
Consider a policy issued to a select life aged [x] under which
premiums and/or annuities are payable continuously and sums
insured are payable immediately on death. Suppose t

8.7 Policy values and Thieles differential equation
tV
(i) :
the policy value at duration t for a policy which is in state i at
that time
(i)
Bt : the rate of payment of benefit while the policyholder is in state
i at time t
(ij)
St : the lump sum benefit

MLC Spring 2015 Written Answer Questions
Model Solutions
1
MLC Spring 2015 Question 1 Model Solution
Learning Objectives: 1(d), 2(a), 3(a), 4(a)
Textbook References: 8.6, 8.7
(a)
a
0j
x:10
)
=
Z
a
00
x:10
10
0
+
0j
t px
a
01
x:10
t
e
+
dt
a
02
x:10
=
01
0