We assume that an individual invests in a financial market with one risklessand one risky asset, with the latter's price following geometric Brownianmotion as in the Black-Scholes model. Under a constant rate of consumption, wefind the optimal investment strategy for the individual who wishes to minimizethe probability that her wealth drops below some fixed proportion of hermaximum wealth to date, the so-called probability of {\it lifetime drawdown}.If maximum wealth is less than a particular value, $m^*$, then the individualoptimally invests in such a way that maximum wealth never increases above itscurrent value. By contrast, if maximum wealth is greater than $m^*$ but lessthan the safe level, then the individual optimally allows the maximum toincrease to the safe level.
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机译：我们假设一个人在金融市场上投资时拥有一种无风险和一种风险资产，其价格遵循Black-Scholes模型中的几何布朗运动。在恒定的消费率下，我们为希望将其财富降至迄今为止最大财富的某个固定比例以下的概率最小化的个人（即所谓的“ \\终身提取”概率）确定了最佳投资策略。小于特定价值$ m ^ * $，那么个人进行最佳投资，以使最大财富永远不会超过其当前价值。相反，如果最大财富大于$ m ^ * $但小于安全水平，则个人最优地允许最大财富增加到安全水平。
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