Generative Bayesian Computation for Maximum Expected Utility

TL;DR

This paper introduces a likelihood-free generative Bayesian method using quantiles and neural estimators to efficiently compute maximum expected utility, demonstrated on portfolio optimization.

Contribution

It presents a novel density-free generative approach with neural quantile estimators for maximum expected utility calculation, applicable to Bayesian decision problems.

Findings

Efficient computation of expected utility via quantile-based generative methods.

Successful application to optimal portfolio allocation with Bayesian learning.

Discussion of links between utility theory and risk-taking behavior.

Abstract

Generative Bayesian Computation (GBC) methods are developed to provide an efficient computational solution for maximum expected utility (MEU). We propose a density-free generative method based on quantiles that naturally calculates expected utility as a marginal of quantiles. Our approach uses a deep quantile neural estimator to directly estimate distributional utilities. Generative methods assume only the ability to simulate from the model and parameters and as such are likelihood-free. A large training dataset is generated from parameters and output together with a base distribution. Our method a number of computational advantages primarily being density-free with an efficient estimator of expected utility. A link with the dual theory of expected utility and risk taking is also discussed. To illustrate our methodology, we solve an optimal portfolio allocation problem with Bayesian learning and a power utility (a.k.a. fractional Kelly criterion). Finally, we conclude with directions for future research.