We investigate a framework for robo-advisors to estimate non-expert clients' risk aversion using adaptive binary-choice questionnaires. We model risk aversion using cost functions and spectral risk measures in a static setting. We prove the finite-sample identifiability and, for properly designed questions, obtain a convergence rate of $\sqrt{N}$ up to a logarithmic factor, where $N$ is the number of questions. We introduce the notion of distinguishing power and demonstrate, through simulated experiments, that designing questions by maximizing distinguishing power achieves satisfactory accuracy in learning risk aversion with fewer than 50 questions. We also provide a preliminary investigation of an infinite-horizon setting with an additional discount factor for dynamic risk aversion, establishing qualitative identifiability in this case.

翻译：本研究探讨了一种机器人顾问框架，该框架通过自适应二元选择问卷来估计非专业客户的风险厌恶程度。我们在静态环境中使用成本函数和谱风险测度对风险厌恶进行建模。我们证明了有限样本的可识别性，并针对合理设计的问题，获得了收敛速度为$\sqrt{N}$（至多相差一个对数因子）的结果，其中$N$为问题数量。我们引入了区分力的概念，并通过模拟实验证明，通过最大化区分力来设计问题，能在少于50个问题的情况下，在学习风险厌恶方面达到令人满意的准确度。我们还对无限时域设定进行了初步探索，其中引入了额外的折现因子以处理动态风险厌恶，并在此情况下建立了定性可识别性。