英文标题：
《General Stopping Behaviors of Naive and Non-Committed Sophisticated
Agents, with Application to Probability Distortion》
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作者：
Yu-Jui Huang, Adrien Nguyen-Huu, Xun Yu Zhou
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最新提交年份：
2019
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英文摘要：
We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time-inconsistent. We study stopping decisions of naive agents who reoptimize continuously in time, as well as equilibrium strategies of sophisticated agents who anticipate but lack control over their future selves\' behaviors. When the state process is one dimensional and the payoff functional satisfies some regularity conditions, we prove that any equilibrium can be obtained as a fixed point of an operator. This operator represents strategic reasoning that takes the future selves\' behaviors into account. We then apply the general results to the case when the agents distort probability and the diffusion process is a geometric Brownian motion. The problem is inherently time-inconsistent as the level of distortion of a same event changes over time. We show how the strategic reasoning may turn a naive agent into a sophisticated one. Moreover, we derive stopping strategies of the two types of agent for various parameter specifications of the problem, illustrating rich behaviors beyond the extreme ones such as \"never-stopping\" or \"never-starting\".
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中文摘要：
我们考虑了一个带有支付函数的扩散过程的停止问题，该函数使得问题时间不一致。我们研究了不断重新优化的天真代理的停止决策，以及预测但无法控制未来自我行为的复杂代理的均衡策略。当状态过程为一维且支付泛函满足一定的正则性条件时，我们证明了任何平衡点都可以作为算子的不动点得到。该操作符表示考虑未来自我行为的战略推理。然后，我们将一般结果应用于代理扭曲概率和扩散过程为几何布朗运动的情况。问题本质上是时间不一致的，因为同一事件的失真程度随时间而变化。我们展示了策略推理如何将一个天真的代理转变为一个复杂的代理。此外，我们还针对问题的各种参数规格推导了这两类代理的停止策略，说明了“从不停止”或“从不启动”等极端行为之外的丰富行为。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Quantitative Finance 数量金融学
二级分类：Economics 经济学
分类描述：q-fin.EC is an alias for econ.GN. Economics, including micro and macro economics, international economics, theory of the firm, labor economics, and other economic topics outside finance
q-fin.ec是econ.gn的别名。经济学，包括微观和宏观经济学、国际经济学、企业理论、劳动经济学和其他金融以外的经济专题
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