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A Robo-Advisor System: expected utility modeling via pairwise comparisons

Bo Chen, Jia Liu

Abstract

We introduce a robo-advisor system that recommends customized investment portfolios to users using an expected utility model elicited from pairwise comparison questionnaires. The robo-advisor system comprises three fundamental components. First, we employ a static preference questionnaire approach to generate questionnaires consisting of pairwise item comparisons. Next, we design three optimization-based preference elicitation approaches to estimate the nominal utility function pessimistically, optimistically, and neutrally. Finally, we compute portfolios based on the nominal utility using an expected utility maximization optimization model. We conduct a series of numerical tests on a simulated user and a number of human users to evaluate the efficiency of the proposed model.

A Robo-Advisor System: expected utility modeling via pairwise comparisons

Abstract

We introduce a robo-advisor system that recommends customized investment portfolios to users using an expected utility model elicited from pairwise comparison questionnaires. The robo-advisor system comprises three fundamental components. First, we employ a static preference questionnaire approach to generate questionnaires consisting of pairwise item comparisons. Next, we design three optimization-based preference elicitation approaches to estimate the nominal utility function pessimistically, optimistically, and neutrally. Finally, we compute portfolios based on the nominal utility using an expected utility maximization optimization model. We conduct a series of numerical tests on a simulated user and a number of human users to evaluate the efficiency of the proposed model.

Paper Structure

This paper contains 18 sections, 1 theorem, 42 equations, 9 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Static preference questionnaire
  3. Assumptions of SPQ
  4. SPQ
  5. Preference elicitation via pairwise comparison
  6. Pessimistic estimation
  7. Optimistic estimation
  8. Neutral estimation
  9. Utility maximization
  10. Numerical test
  11. Test setting
  12. Simulation results: comparison between SPQ and randomly generated questionnaires
  13. Simulation results: convergence of nominal utility functions to the true utility function
  14. Simulation results: investment process driven by the robo-advisor
  15. Application to human users: elicited utility
  16. ...and 3 more sections

Key Result

Lemma 1

The set $L_{K}$ is a one-point set if and only if

Figures (9)

  • Figure 1: Flowchart of the robo-advisor system
  • Figure 2: Flowchart of the static preference questionnaire generation method
  • Figure 3: Nominal preference elicitation process
  • Figure 4: Nominal utility functions (pessimistic, optimistic, neutral estimations) elicited by using SPQ and randomly generated questionnaires
  • Figure 5: Nominal utility functions (pessimistic, optimistic, neutral estimation) elicited by different numbers of questions generated randomly
  • ...and 4 more figures

Theorems & Definitions (2)

  • Lemma 1
  • proof