We show that the mutual fund theorems of Merton (1971) extend to the problem of optimal investment to minimize the probability of lifetime ruin. We obtain four such theorems by considering a financial market both with and without a riskless asset and by considering both constant and random consumption.
We show that the mutual fund theorems of Merton (1971) 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 consumption. The striking result is that we obtain two-fund theorems despite the additional source of randomness from consumption.
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