EPVs using transition rates

[Alfie]

Hi, Feeling stuck on finding the EPV when using transition rates to find EPVS. sometimes the solutions do transition probability x force of transition, and sometimes they just use transition probability. Im looking at chapter 24.6, only the death benefit includes force of transition, but i dont understand why the sickness benefits could not also be 'transition probability to stay in h x force of transition to sick' etc. Can someone help please? Thank you

 

[Alfie]

Hi, Feeling stuck on finding the EPV when using transition rates to find EPVS. sometimes the solutions do transition probability x force of transition, and sometimes they just use transition probability. Im looking at chapter 24.6, only the death benefit includes force of transition, but i dont understand why the sickness benefits could not also be 'transition probability to stay in h x force of transition to sick' etc. Can someone help please? Thank you

... and then in question 9 it doesnt invole transition intensities at all but instead just uses the probabilities - is this something to do with it not being continuous payments? or is it just because there is only a small no of years so we can sum it manually

 

[Michael Clarkson]

Hi Alfie,

If you used "probability to stay in h x force of transition to sick" within the integral you would calculate the EPV of a benefit that is paid just at the points the individual transitions from healthy to sick. However, for question 24.6, the benefit is continuously paid whenever the individual is sick. So we need the probability that the currently healthy life is sick at time r (r_p^ht_45). The benefit amount is then discounted back to time 0, and we integrate over all points in time at which a benefit could be paid.

Transition intensities are needed for death benefits that are paid immediately because the death benefit could be paid at any possible moment in time. So we need the probability of dying at time t (tpx * mu_x+t) and then integrate over all possible points in time when death might occur. For Q9, we don't need to use an integral / transition intensities because we only have 2 years so can sum it manually. The death benefit can only be paid at the end of the 1st of 2nd year so we can just calculate EPV of death benefit as {probability of dying in first year * v} + {probability of dying in second year * v^2}... and we can take a similar approach for the EPV of the premiums, expenses etc.

Hope helpful
Michael