Description: In this expository paper several comments are made with respect to the statistical independence of the curtate future lifetime and the fractional part of the future lifetime, both of a general status. In particular, the conditions for independence need to be stated carefully. The last-survivor status is cited as an example. More general assumptions than the uniform distribution of deaths assumption are then considered, together with applications to insurances, annuities, and reserves. Similar results to those under the uniform distribution of deaths assumption are obtained. Brief comments are made with respect to contingent probabilities in multiple lives and multiple decrement theory.

Description: In this paper, we derive three important longevity Greeks on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility.

Description: In this paper, we derive three important longevity Greeks on the basis of an extended version of the Lee-Carter model that incorporates stochastic volatility.