Risk, Ambiguity and Dynamic Choice

本课题研究了不确定条件下决策中的两个不同问题。第一个问题涉及随着时间的推移不确定性的解决。个人的选择不仅反映了他们对不确定的最终结果的担忧，也反映了他们对这种不确定性将如何随着时间的推移而解决的兴趣。我们开发了一种新的时间不确定性解决偏好模型，该模型比现有模型更简单，更接近许多标准的经济和金融动态模型，因此需要更少的关于个人对未来的信念的数据。我们的第二个项目涉及模糊性；也就是，个人发现难以量化他们所面临的不确定性的情况。我们提出了一个框架，在这个框架中，决策者区分明确和模糊的事件，并使用前者来校准后者。因此，每个明确的事件A由两个事件校准，最不可能的明确事件比A更有可能，而最有可能的明确事件比A更不可能。我们的目标是发展一种主观的(即，基于偏好的)不确定性理论，它允许模糊感知，但又服从概率论和统计学的适当修改版本。不确定性的时间分解模型和模糊性模型在宏观经济学和金融学中都有很多应用。这两条调查路线都受到开发和测试模型的困难的限制。我们的更简单的模型应该会促进这些应用，并使其更容易识别其参数和找到相关的经验证据。我们的不确定性时间分辨率模型不同于Kreps和Porteus的模型，它允许优先选择早期分辨率，而不需要对不影响基本面的高阶信息敏感；它类似于不优先选择分辨率时机的标准动态模型。在这样的模型中，决策者在每个时期从她在那个时期可能的随机消费中获得效用。在我们的模型中，决策者只从她对最终消费的信念中获得效用，而不是从她对信念将如何演变的信念中获得效用。这部分研究的目的如下：(一)提供风险消费偏好的公理基础。(2)制定和分析适当的优惠措施，以便及早/推迟解决不确定性。(3)调查风险消费偏好在各种应用中的影响。我们的校准歧义模型提供了一个新的概念歧义感知(我们称之为定性不确定性关系)。我们的主要结果建立了定性不确定性的内部概率表示，类似于Dempster-Shafer理论。为了能够区分模糊感知和模糊态度，我们允许定性的不确定性关系是不完备的。这种不完备性反映了这样一个事实，即当存在模棱两可时，决策者本身对模棱两可的感知不足以决定她的赌注排名。本研究的目的是提供一个定性不确定性关系的表示定理，并用它来研究更新、推理以及现有的歧义模型和证据模型之间的关系。

This project studies two different problems in decision making under uncertainty. The first deals with the resolution of uncertainty over time. The choices that individuals make reflect not only their concern for the uncertain ultimate outcome but also their interest in how this uncertainty will resolve over time. We develop a new model of preference for temporal resolution of uncertainty that is simpler than existing models, closer to many standard dynamic models of economics and finance and, therefore, requires less data on individuals' beliefs about the future. Our second projects deals with ambiguity; that is, situations in which individuals find it difficult to quantify the uncertainty they are confronting. We propose a framework in which decision makers distinguish between unambiguous and ambiguous events and use the former to calibrate the latter. Thus, each unambiguous event, A, is calibrated by two events, the least likely unambiguous event more likely than A and the most likely unambiguous event less likely than A. Our goal is to develop a subjective (i.e., preference-based) theory of uncertainty that permits ambiguity perception and yet is amenable to suitably modified versions of probability theory and statistics. Models of temporal resolution of uncertainty and models of ambiguity both have many applications in macroeconomics and finance. Both of these lines of inquiry are limited by difficulties in developing and testing models. Our simpler models should facilitate these applications and make it easier to identify their parameters and find the relevant empirical evidence.Our model of temporal resolution of uncertainty differs from the Kreps and Porteus' model by allowing for preference for early resolution without requiring sensitivity to higher order information that does not affect fundamentals; it is analogous to standard dynamic models of choice without preference for timing of resolution. In such models, the decision maker derives utility each period from her possibly random consumption in that period. In our model, the decision maker derives utility only from her beliefs about what she will ultimately consume, not from her beliefs about how her beliefs will evolve. This part of the research has the following goals: (i) provide an axiomatic foundation of risk consumption preferences. (ii) Develop and analyze appropriate measures of preference for early/late resolution of uncertainty. (iii) Investigate the implications of risk consumption preferences in various applications. Our model of calibrated ambiguity offers a new notion ambiguity perception (which we call qualitative uncertainty relations). Our main result establishes an inner probability representation for qualitative uncertainty analogous to the Dempster-Shafer theory. To be able to distinguish ambiguity perception from ambiguity attitude, we allow the qualitative uncertainty relation to be incomplete. This incompleteness reflects the fact that when there is ambiguity, a decision maker's perception of ambiguity by itself, is not sufficient to determine her ranking of bets. The goal of this research is to provide a representation theorem for qualitative uncertainty relations and use it to study updating, inference and the relationships among existing models of ambiguity and evidence.