This paper proposes a novel framework for identifying an agent's risk aversion using interactive questioning. Our study is conducted in two scenarios: a one-period case and an infinite horizon case. In the one-period case, we assume that the agent's risk aversion is characterized by a cost function of the state and a distortion risk measure. In the infinite horizon case, we model risk aversion with an additional component, a discount factor. Assuming the access to a finite set of candidates containing the agent's true risk aversion, we show that asking the agent to demonstrate her optimal policies in various environment, which may depend on their previous answers, is an effective means of identifying the agent's risk aversion. Specifically, we prove that the agent's risk aversion can be identified as the number of questions tends to infinity, and the questions are randomly designed. We also develop an algorithm for designing optimal questions and provide empirical evidence that our method learns risk aversion significantly faster than randomly designed questions in simulations. Our framework has important applications in robo-advising and provides a new approach for identifying an agent's risk preferences.

翻译：本文提出了一种新颖的框架，通过交互式提问来识别智能体的风险厌恶程度。我们的研究在两个场景中进行：单期情形和无限期情形。在单期情形中，我们假设智能体的风险厌恶由其状态成本函数和扭曲风险度量表征。在无限期情形中，我们增加了折现因子这一成分来对风险厌恶建模。假设可以访问一个包含智能体真实风险厌恶值的有限候选集，我们证明，让智能体在不同环境中（可能基于其先前回答）展示其最优策略，是识别其风险厌恶的有效手段。具体来说，我们证明当提问次数趋于无穷且问题随机设计时，智能体的风险厌恶可以被识别。我们还开发了一种设计最优问题的算法，并通过仿真提供经验证据，表明我们的方法学习风险厌恶的速度显著快于随机设计的问题。我们的框架在机器人投顾领域具有重要应用，并为识别智能体风险偏好提供了一种新途径。