Independent to dependent probabilities - Profit testing

[Sid Kumar]

What is the right approach to use on the exam? the approximation/simplified calculations or to derive the force of transitions from the independent rates to then derive the dependent probabilities.

It seems as though there is a bit of flip flopping in the ActEd materials and the past question papers (going back to 2005) on WHEN and HOW the dependent probabilities should be calculated. For simple two decrement case of deaths and surrender/withdrawal, in some instances (including ActEd notes 2018), a benefit costs are computed using independent mortality rates without converting to dependent, however converting independent surrender rates to dependent using (1-Qxd)*Independent surrender rate = Dependent surrender rate (As shown for Example 3: on page 23 CT5-12 Profit Testing). I call this the simplified/approximation for brevity

Both questions below include the following wording: On surrender or on survival to the end of the term, the bid value of the units is payable at the end of the year of exit.

In April 2006 Q 14 the profit test decrement table is as shown: simplified/approximation for brevity




In the April 2005 Q13 solution the decrement probabilities shown are based on conversion to dependent probabilities for both death and surrender. Here the dependent probabilities appear to be based on first calculating the force of transitions and then using the (aq)x calculations from force of transitions.

 

[Harashima Senju]

I would think this only applies when you are told that the surrenders only occur at the end the year. Otherwise we would have to derive the dependent probabilities of surrender using the forces of decrement which we assume are constant between integer ages

 

[Mohit Gulati]

if they say that surrender occur only at the end of year then death probability will be an independent probability but surrender probability will be a dependent probability , since only those people will surrender who will survive. whereas when they say surrender can occur throughout the year, then both death and surrender probability will be dependent.

in the second case when both the death and surrender probability are dependent so you will have to derive those probability using the kolomogorov closed formula given in chapter 10.

for kolmogorov formula you need force of surrender and force of mortality which will be given in question.

if force of mortality is not given in question, so they will specify the table from which you will take the survival probability and
from that survival probabaility you will calculate the force of mortality.

force of mortality = -ln(survival probability) provided the force is assumed to be constant throughout the year.

 

[Harashima Senju]

In the first case why will surrender probability be a dependent probability if it occurs only at the end of year? Do we have to derive the dependent probability of surrender using the Kolmogorov closed form formula?

 

[Mohit Gulati]

no it will be dependent in the sense that it will depend upon how much people survive because only survived people will surrender, but in order to calculate that you donot need to use kolgmogorov closed form. korlmogorv will be used when both the surrender and deaths are occurring throughout the year.

 

[Harashima Senju]

Thanks