Inference of Utilities and Time Preference in Sequential Decision-Making

TL;DR

This paper develops a new stochastic control framework to accurately infer individual investment preferences from past activities, improving robo-advisors' personalization by modeling utility, discounting, and addressing time inconsistency.

Contribution

It introduces a continuous-time model with a novel approach to infer client preferences, including a learning algorithm with proven convergence, and demonstrates practical effectiveness through numerical examples.

Findings

Effective inference of client preferences in investment models

Convergence of the proposed maximum likelihood learning algorithm

Successful numerical validation with Merton's problem

Abstract

This paper introduces a novel stochastic control framework to enhance the capabilities of automated investment managers, or robo-advisors, by accurately inferring clients' investment preferences from past activities. Our approach leverages a continuous-time model that incorporates utility functions and a generic discounting scheme of a time-varying rate, tailored to each client's risk tolerance, valuation of daily consumption, and significant life goals. We address the resulting time inconsistency issue through state augmentation and the establishment of the dynamic programming principle and the verification theorem. Additionally, we provide sufficient conditions for the identifiability of client investment preferences. To complement our theoretical developments, we propose a learning algorithm based on maximum likelihood estimation within a discrete-time Markov Decision Process framework, augmented with entropy regularization. We prove that the log-likelihood function is locally concave, facilitating the fast convergence of our proposed algorithm. Practical effectiveness and efficiency are showcased through two numerical examples, including Merton's problem and an investment problem with unhedgeable risks. Our proposed framework not only advances financial technology by improving personalized investment advice but also contributes broadly to other fields such as healthcare, economics, and artificial intelligence, where understanding individual preferences is crucial.