General stopping behaviors of naïve and noncommitted sophisticated agents, with application to probability distortion
General stopping behaviors of naïve and noncommitted sophisticated agents, with application to probability distortion
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DOI：
10.1111/mafi.12224
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发表时间：
2017-09
影响因子：
1.6
通讯作者：
Yu‐Jui Huang;A. Nguyen-Huu;X. Zhou
中科院分区：
文献类型：
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作者：
Yu‐Jui Huang;A. Nguyen-Huu;X. Zhou
我们考虑了停止一个扩散过程的问题，该扩散过程具有一个使问题时间不一致的支付泛函。我们研究了不断重新优化的幼稚代理人的停止决策，以及预测但缺乏对未来自我行为控制的复杂代理人的平衡策略。当状态过程是一维的，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。这个操作符代表考虑未来自我行为的策略推理。然后，我们将一般结果的情况下，代理扭曲的概率和扩散过程是一个几何布朗运动。这个问题本质上是时间不一致的，因为同一事件的失真程度会随着时间的推移而变化。我们展示了战略推理如何将一个天真的代理人变成一个复杂的代理人。此外，我们推导出两种类型的代理的停止策略的各种参数规格的问题，说明丰富的行为超出极端的，如“永不停止”或“永不启动”。
We consider the problem of stopping a diffusion process with a payoff functional that renders the problem time‐inconsistent. We study stopping decisions of naïve 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 naïve 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.”