朴素和非承诺的复杂代理的通用停止行为，及其在概率扭曲中的应用
General Stopping Behaviors of Naive and Non-Committed Sophisticated Agents, with Application to Probability Distortion
AI总结：
本文研究了在时间不一致的收益函数下停止扩散过程的问题，分析了朴素代理的连续再优化决策和复杂代理的均衡策略，并探讨了概率扭曲对停止策略的影响。
摘要：
我们考虑了具有使问题时间不一致的收益函数的停止扩散过程的问题。我们研究了朴素代理的停止决策，这些代理在时间上持续再优化，以及复杂代理的均衡策略，这些代理预见到但无法控制未来自我行为。当状态过程是一维且收益函数满足某些正则性条件时，我们证明任何均衡都可以作为算子的不动点获得。该算子代表了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且扩散过程为几何布朗运动的情况。该问题本质上是时间不一致的，因为相同事件的扭曲水平随时间变化。我们展示了战略推理如何将朴素代理转变为复杂代理。此外，我们为两种类型的代理推导了各种参数规格问题的停止策略，展示了超越“永不停止”或“永不开始”等极端行为的丰富行为。
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".
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
