A mixed blessing of lifespan heterogeneity

On the effects of changing mortality patterns on investment, labour and consumption under uncertainty

“…Equation 9shows that in difference to the classical wealth equation, the drift rate r t is replaced by the yield of the actuarial note r t + ν t . 12 As the analysis above has shown, the problem (1) of the finitely lived agent subject to constraint (9), is equivalent to the problem (4) of an infinitely lived agent subject to constraint (9), where the discount rate as well as the drift of the wealth process have been adjusted to accommodate the mortality risk. In order for the stochastic optimal control problem to be well defined and to simplify our arguments, we assume that the deterministic functions r t and ν t as well as there (possibly piecewise) derivatives are bounded, the wage process w t is bounded on every interval [0, T ]] and the controls π t , C t and L t are progressively measurable L 2 -processes on every interval [0, T ].…”

“…More recently, Gahramanov and Tang (2013) have presented a paper in which they considered the retirement problem in a continuous time model with time varying mortality. However their work differs from ours, in that they focused on the retirement problem with mortality being given by an explicit analytic function as in Feigenbaum (2008).…”