# Multiple state model - benefits payable at end of year

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Hi

Why are integrals used to evaluate the EPV of benefits here, when the benefits are payable at the end of the year? Shouldn't summation be used instead?

by (670 points)
Hi

If summation is used, it will imply that transition from healthy state to dead state will only take place at any integer time interval (i.e. in 1 year time, 2 years time etc.). This implies that deaths occurring in between integer time intervals will receive no benefit, which is not true. For example, death in 1.5 years time will still receive at end of the year in which death occurs.

Integration will include all the transitions from healthy state to dead state that take place in between integer time intervals. Hence, integration used.
by (1.1k points)
edited by
Thanks! How does the memo's answer account for the fact that the benefits are payable at the end of the year though, as it is discounting the cashflow as if it was paid immediately?
by (2.9k points)
It appears to be an error in the question but we cannot say for sure as we were not involved in setting the question (nor were we taught by whoever taught the content which makes it difficult to comment on whether or not to say it is an error or if we have missed something).

If payments are made at the end of the year, you can mix both integrals and summations (so sum each continuous year). Otherwise, from the questions you are more likely to handle, it's as normal with payments occurring at the date of death (using the usual integral we know and love).