Utility theory front to back - inferring utility from agents' choices

TL;DR

This paper investigates whether observed consumption and investment behaviors can be used to infer the underlying utility functions of agents, providing conditions and methods in both deterministic and stochastic continuous-time models.

Contribution

It introduces an inverse approach to utility theory, deriving utility functions from observed strategies, and characterizes the conditions under which strategies are consistent with utility maximization in continuous-time models.

Findings

Multiple utility functions can generate the same consumption pattern in deterministic models.

In stochastic models, strategies must satisfy a specific PDE to be consistent with utility maximization.

Risk attitudes like DARA can be inferred directly from observed consumption and investment choices.

Abstract

We pursue an inverse approach to utility theory and consumption & investment problems. Instead of specifying an agent's utility function and deriving her actions, we assume we observe her actions (i.e. her consumption and investment strategies) and ask if it is possible to derive a utility function for which the observed behaviour is optimal. We work in continuous time both in a deterministic and stochastic setting. In the deterministic setup, we find that there are infinitely many utility functions generating a given consumption pattern. In the stochastic setting of the Black-Scholes complete market it turns out that the consumption and investment strategies have to satisfy a consistency condition (PDE) if they are to come from a classical utility maximisation problem. We show further that important characteristics of the agent such as her attitude towards risk (e.g. DARA) can be deduced directly from her consumption/investment choices.