Maximum Expected Utility by MCMC

Eric Jacquier
MIT Sloan and HEC Montreal

Michael Johannes
Graduate School of Business, Columbia University

Nicholas Polson
Graduate School of Business, University of Chicago


This paper provides a new simulation-based approach to maximum expected utility (MEU) portfolio allocation problems. MEU requires computation of expected utility and its optimization over the decision variable. In portfolio problems, the expected utility is generally not analytically available. Traditional methods use gradient-based estimates of expected utility, leading to computational inefficiencies that are particularly acute in portfolio problems with parameter uncertainty (i.e. estimation risk). Our simulation-based method avoids the calculation of derivatives and also allows for functional optimization. The algorithm combines Markov Chain Monte Carlo (MCMC) with the insights of simulated annealing and evolutionary Monte Carlo. It can exploit conjugate utility functions and latent variables in the relevant predictive density for efficient simulation. We also show how slice sampling naturally allows for constraints in the portfolio weights. We illustrate our methodology with a portfolio problem with estimation risk and CARA utility.