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Optimal Investment and Consumption Decisions when Time-Horizon is Uncertain

Many investors do not know with certainty when their portfolio will be liquidated. Should their portfolio selection be in‡uenced by the uncertainty of exit time? In order to answer that question, we consider a suitable extension of the familiar optimal investment problem of Merton (1971), where we allow the conditional distribution function of an agent’s time-horizon to be stochastic and correlated to returns on risky securities. In contrast to existing literature, which has focused on an independent time-horizon, we