aversion $b(t)$. [@Steffensen2011] provides a first insight into the optimal policy when the utility parameters of the intertemporal utility, which is of a CRRA type, are time-varying; thus $a(t)$ and $b(t)$ are captured. But the model disregards terminal wealth, consumption floor and labor income. In a similar fashion, [@Hentschel2016] studies the consumption problem for CRRA utility with habit formation and considers $a(t)$ and $b(t)$. Similar to [@Steffensen2011], neither terminal wealth nor consumption floor nor income are included in their model. Finally, [@Aase2017] uses the martingale method (that allows to reformulate the optimal stochastic control problem to a simpler maximization problem with constraint) to determine optimal consumption and investment under mortality and a CRRA utility with age-depending risk aversion $b(t)$. But the model does not consider terminal wealth, consumption floor, income or time-varying preference $a(t)$.

The main contributions and innovations of this paper can be summarized as follows: we consider all the ‘ingredients’ of the models in the above mentioned papers ($a(t)$, $b(t)$, terminal wealth, floors for consumption and terminal wealth via HARA utilities, income process) that leads to a novel, very flexible and more realistic dynamic life-cycle model framework. We extend or generalize [@Ye2008] by adding an age-dependent coefficient of 