Ct5: Chap 9

How to solve part(ii) of below ques?
Mortality profit for joint life?

 

This is the ques

 

Consider 3 cases:
1)Both M & F alive
2)only M alive
3)only F alive
For Each case find reserve at the end of the year.
Case 1:
Find Actual Death strain,Expected Death Strain and Mortality profit=EDS-ADS
Case 2:
Here we consider policies out of joint lives in which only female dies(10policies) so reserve for those males=reserve for male(which is always greater than reserve for joint)-reserve for joint.[THIS IS DEATH STRAIN]
Find ADS,EDS and Mortality profit.
Case 3:
Here we consider policies out of joint lives in which only male dies(20 policies) so reserve for those males=reserve for female(which is always greater than reserve for joint)-reserve for joint.[THIS IS DEATH STRAIN]
Find ADS,EDS and Mortality profit.

Add the profits of all cases considered.

Alternatively
You know profit=premiums collected-claims paid-reserves set side.
1)Premium collected=P*no of policies*(1+i) [premiums collected at start but accumulated at end of the year to calculate profit so (1+i)]

2)claims paid=no of policies in which both lives die*claim amount*(1+i)^.5 [claims are expected to occur uniformly over the year]

3)Reserve set aside=Nm*Vf+Nf*Vm+Nmf*Vmf
where Nm=no of policies in which only male dies
Vf=reserve set aside for policies where female survives
Nf=no of policies in which only female dies
Vm=reserve set aside for policies where male survives
Nmf=no of policies in which both survives
Vf=reserve set aside for policies where both survives

 

Not clear..can u please xplain calculation with general reasoning??

 

Steps..
1) Calculate Reserve at the year end Assuming both survive

\(1V = 100000 \require{enclose}\bar A_{61:56} - P \require{enclose}\ddot{a}_{61:56}\)
(Please note there is bar above 61:56)
Now consider the cases

Case 1) Both die

DSAR = \(100000 - 1V\)
Expected DS = \(10000 * q_{60} * q_{55} * DSAR\)
ADS - Only one policy where both died so
ADS = DSAR
hence mort. profit = EDS - ADS

Case 2) Male Die and female survive

In this case we need to calculate reserve only for female life
\(1V^{f} = 100000 \require{enclose}\bar A_{56} - P \require{enclose}\ddot{a}_{56} \)
DASR for female = \(1V^{f} - 1V^{both}\)
Where \(1V^{Both}\) is the reserve assuming both survive
EDS = \( 10000 * q_{60} * p_{55} * DSAR\)
ADS = \(20 * DSAR for female \)

Case 3) Female Die, Male survive
Repeat steps in case 2 for male.
Finally add all Mortality profits.
Best Luck

 

Hey.
Sorry for late reply.
.
In Case 2: female survives and Male dies;
DSAR=1V(female) - 1V(both)
.
What it the reason behind that?
Please explain.

 

Sorry for late.
In case of last survive, SA will be paid on last death,
Case 2 and 3
If single life to die then there is no need to pay SA. Hence we can't use
DSAR = SA - tV
Contract needs to pay the shortfall between the individual to both ( if both survive)

 

Okay..thnq!