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摘要翻译：
在这篇文章中，我们研究了一个最优停止/最优控制问题，该问题是一个风险规避者在何时出售资产时所面临的决策模型。市场是不完整的，因此资产敞口无法对冲。除了决定何时出售之外，代理人还必须选择一个与可行的财富过程相对应的控制策略。我们把这个问题表述为一个涉及停止时间和鞅的选择的问题。我们猜想解的形式，并验证候选解等于值函数。该解的有趣之处在于，它以一种非常明确的形式可用，对于某些参数值，最优策略比最初预期的更复杂，而且尽管设置是基于连续扩散的，但最优鞅可能涉及一个跳跃过程。对该解的一种解释是，风险厌恶主体进行赌博是最优的。
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英文标题：
《An explicit solution for an optimal stopping/optimal control problem
which models an asset sale》
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作者：
Vicky Henderson, David Hobson
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最新提交年份：
2008
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
In this article we study an optimal stopping/optimal control problem which models the decision facing a risk-averse agent over when to sell an asset. The market is incomplete so that the asset exposure cannot be hedged. In addition to the decision over when to sell, the agent has to choose a control strategy which corresponds to a feasible wealth process. We formulate this problem as one involving the choice of a stopping time and a martingale. We conjecture the form of the solution and verify that the candidate solution is equal to the value function. The interesting features of the solution are that it is available in a very explicit form, that for some parameter values the optimal strategy is more sophisticated than might originally be expected, and that although the setup is based on continuous diffusions, the optimal martingale may involve a jump process. One interpretation of the solution is that it is optimal for the risk-averse agent to gamble.
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PDF链接：
https://arxiv.org/pdf/0806.4061
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