This thesis consists of three essays. In Precautionary Saving under Correlated Risk, I show that the sign of the correlation between the random variables might determine whether saving increases or decreases when risk is introduced. Precautionary saving is thus not confirmed. In the second part of this chapter, the consumer must also allocate her saving between an insurance and an interest-bearing asset. It is shown that switching the sign of correlation changes the optimal insurance ratio and probably also optimal saving. Saving and Portfolio Choice by Mutually Altruistic Consumers treats the effects of mutual altruism between two individuals. Compared to the Utilitarian social optimum there is, on the one hand, a tendency to higher saving and lower risk share resulting from the higher uncertainty of future income in the Nash equilibrium. On the other hand, there is a tendency to lower saving and higher risk share arising from the possibility of a free ride on the generosity of others, named "Samaritan's Dilemma". Analytically, it was not possible to determine the size or the direction of divergences in the choice variables. Numerical examples show that the effect of the Samaritan's Dilemma outweighs the effect of the greater uncertainty of future income in the Nash equilibrium. However, the divergence in saving between the two solutions is rather small. In the literature, uncertain lifetime has been used to explain both unexpectedly low and unexpectedly high saving by the elderly. In The Effect of Uncertain Lifetime on the Saving of the Elderly, risk is introduced into the remaining lifetime and the consequences of a background risk are investigated. Introducing uncertain lifetime into the certainty model results in a slower decumulation of wealth from the date of retirement. On the contrary, introducing uncertain lifetime into a model with uncertain investment income results in a swifter decumulation and an earlier depletion of wealth.