Inference of Utilities and Time Preference in Sequential Decision-Making
This work addresses personalized investment advice for financial technology, with potential applications in healthcare and AI, but it is incremental as it builds on existing stochastic control and MDP methods.
The paper tackles the problem of inferring clients' investment preferences from past activities for robo-advisors, introducing a stochastic control framework that incorporates utility functions and time-varying discounting, with results including theoretical identifiability conditions and a learning algorithm shown to be effective in numerical examples like Merton's problem.
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.