We show that the mutual fund theorems of Merton [1971. Journal of Economic Theory 3, 373-413] extend to the problem of optimal investment to minimize the probability of lifetime ruin. We obtain two such theorems by considering a financial market both with and without a riskless asset for random...

In this paper, we explicitly solve the problem of maximizing utility of consumption (until the minimum of bankruptcy and the time of death) with a constraint on the probability of lifetime ruin, which can be interpreted as a risk measure on the whole path of the wealth process.