Longevity and health risks in a three-state Markov model with focus on disability and retirement

Specialeforsvar ved Bolette Linding Nielsen

Titel: Longevity and health risks in a three-state Markov model with focus on disability and retirement

Abstract: This thesis presents an analysis of longevity and health risks in a three-state Markov chain without re-activation. The framework consists of two transition intensity-foundations: the historical G82-foundation and the 2017-mortality from the Danish Financial Supervisory Advisory (DFSA), accompanied by a disability intensity from the life insurance company PFA. The two foundations are compared and applied to construct the related transition probabilities of the Markov chain, from which the active- and alive-time are constructed, as well as the ratio between the two. Particularly the ratio confirms the suspicion that an additional year living does not equal a full healthy year.
We furthermore investigate the expected remaining lifetime, and its sensitivity to changes in the longevity improvements. This is done by differentiating the ordinary differential equations of the transition probabilities with respect to an added constant, which extends the longevity improvement-function. The method of differentiation is borrowed from [18], and adjusted to the purpose of this thesis. We find that we are indeed quite sensitive to changes in the longevity, which prompts us to consider the observed historical kink in the Danish expected remaining lifetimes in the late 20th century. We investigate a possible relation between the kink and the longevity improvements, and find that the kink could be attributed to the improvements on a purely theoretical basis.
Moving the focus from longevity to health, we consider the possibility of expanding the applied disability intensity to be modelled like the DFSA-mortality, i.e. a Lee-Carter model. We discuss the introduction of possible "health" improvements, their construction, and possible dependence or independence of the longevity improvements. Finally we consider four criteria for constructing a new retirement age-function. By considering the mortality-sensitivity of the criteria, we obtain ordinary, non-linear differential equation systems for the retirement age-functions depending on the mortality. No solutions are found to these - neither numerically nor analytically, and so the thesis is ended with a discussion of a simpler method of construction.

 

Vejleder:  Mogens Steffensen
Censor:    Magnus Tor Ry Hessler, Danica Pension