标题： 具有消费棘轮和回撤约束的不完全半鞅市场中的效用最大化 显示英文标题

标题： Utility maximization with ratchet and drawdown constraints on consumption in incomplete semimartingale markets

摘要： 在本文中，我们使用对偶方法研究在消费的爬行和回撤约束下的期望效用最大化问题，在一个一般的不完全半鞅市场中。 优化问题是相对于两个参数进行的：初始财富和消费过程的实质下界。 为了陈述问题并定义原始域，我们引入了运行最大值概念到任意非负可选过程的自然扩展，并研究其性质。 优化的对偶域是根据在非负可选过程集上引入的一种排序关系下的坚实性来表征的。 我们为优化问题获得的抽象对偶结果用于推导完全市场情况下的解的更详细表征。 显示英文摘要

摘要： In this paper, we study expected utility maximization under ratchet and drawdown constraints on consumption in a general incomplete semimartingale market using duality methods. The optimization is considered with respect to two parameters: the initial wealth and the essential lower bound on consumption process. In order to state the problem and define the primal domains, we introduce a natural extension of the notion of running maximum to arbitrary non-negative optional processes and study its properties. The dual domains for optimization are characterized in terms of solidity with respect to an ordering that is introduced on the set of non-negative optional processes. The abstract duality result we obtain for the optimization problem is used in order to derive a more detailed characterization of solutions in the complete market case.