our proposed model can explain and describe people’s observed behavior of reducing relative risky investments by time while simultaneously targeting a certain function for the consumption rate on average. In opposite, we find that the previously described existing models are not able to capture this behavior. Therefore, particulary Section \[sec:NCS\] shows that it is economically important to have separate functions or parameters for risk aversion and preference of consumption over terminal wealth, $a(t)$ and $b(t)$.

In addition, consumption and wealth floors are introduced which have an economic meaning as minimum required levels of consumption and wealth. This motivates the development of a dynamic life-cycle model with time-varying risk preferences such as coefficient of risk aversion and consumption and wealth floors which can capture age-depending consumption and investment behavior of investors.

Related literature to this topic consider stochastic income and unemployment risks, see [@BodieMertonSamuelson1992], [@Koo1998], [@Munk2000], [@Viceira2001], [@Huang2008], [@Jang2013], [@Bensoussan2016], [@Wang2016] or [@Chen2018]. Setups where the investor faces uncertain lifetime, mortality and optimal life insurance are considered in [@Yaari1965], [@PliskaYe2007], [@MenoncinRegis2017], [@ZouCadenillas2014], [@KronborgSteffensen2015], [@ShenWei2016], [@Duarte2011], [@Huang2012], [@KronborgSteffensen2015], [@ShenWei2016] and [@Ye2008]; optimal consumption and investment under insurer default risk is studied by [@JangKooPark2019]. [@KraftMunk2011], [@KraftMunkWagner2018], [@AndreassonShevchenkoNovikov2017], [@CuocoLiu2000] and [@DamgaardFuglsbjergMunk2003] analyze optimal housing 