Hi all Please anyone help me to understand how can I calculate dependent probabilities of death and surrender from the independent ones ? I know one method that is to calculate force of transitions using independent probabilities first and then dependent probabilities using that forces. But this method is very lengthy and in the solution, they haven't mentioned how they have calculated. Is there any other method to do it? Any direct relation in qx and (aq)x ?
The method you mention (calculating the forces from the independent probabilities, and then using the forces to calculate the dependent ones) is the correct method. There is no direct relationship between qx and (aq)x other than through the forces of decrement. (Note that another method for calculating dependent probabilities from independent probabilities used to be included in the course, but it is no longer on the syllabus.)
yes, you can calculate directly using the formula given on page number 35 in Formulae and Tables book. The formula given is for three decrements but you can use it for two as well by removing the last term of the formula(1/3 qxbeta qxgamma). I've calculated using this only.
No, you can't. That is the old method, I mentioned in my original post. It is no longer on the syllabus.
It means we have to use that lengthy method of getting dependent probabilities from independent ones even in the long questions of Profit Testing?
However, sometimes in profit testing questions, surrenders only occur at the end of the year. In this case the dependent mortality probability is the same as the independent probability, and the dependent surrender probability is just the probability of surviving multiplied by the probability of surrendering at the end of the year.
