Eliciting Risk Aversion with Inverse Reinforcement Learning via Interactive Questioning

TL;DR

This paper presents a method for estimating clients' risk aversion using adaptive questionnaires, achieving accurate results with fewer than 50 questions by maximizing distinguishing power.

Contribution

It introduces a framework combining inverse reinforcement learning and adaptive questioning to efficiently identify risk preferences, including static and dynamic models.

Findings

Finite-sample identifiability proven for static models

Convergence rate of √N up to log factor with well-designed questions

Effective risk aversion estimation with fewer than 50 questions

Abstract

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.