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       Department of Systems Engineering and Engineering Management



                          The Chinese University of Hong Kong



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Date: Monday, June 16, 15:00 pm – 16:00 pm



Venue: ERB 513, The Chinese University of Hong Kong



Speaker: Professor Jia Liu, Xi'an Jiaotong University



Title: Eliciting Von Neumann–Morgenstern utility from discrete choices 

with response error



Abstract: We investigate the elicitation method for the Von 

Neumann–Morgenstern (VNM) type decision maker (DM) from pairwise 

comparison data in the presence of response errors. We apply the 

maximum likelihood estimation (MLE) method to elicit the nominal 

utility, together with the variance of the response error, assuming a 

Gumbel distribution. Given the finite support of the pairwise 

comparison lotteries and prior risk-aversion information on the DM, we 

reformulate the MLE as a convex programming problem and establish 

theoretical consistency guarantees. The proposed framework enables 

robust inference of latent utility functions from observed choice 

data. We derive statistical errors between the MLE parameters and the 

true parameters, and we establish the quantitative convergence of the 

MLE VNM utility to the true utility in the sense of the Kolmogorov 

distance. We demonstrate that the optimization problem maximizing 

expected MLE VNM utility is robust against the response error in a 

probabilistic sense. Numerical results validate the practicality of 

the MLE method in a portfolio selection application.



Bio: Jia Liu is an associate professor in the School of Mathematics 

and Statistics at Xi'an Jiaotong University. His research interests 

include stochastic optimization, robust optimization, financial 

models, and financial optimization. He has achieved some notable 

research results in multi-stage distributionally robust portfolio 

selection and chance constrained optimization with applications in 

finance. He has published more than 40 papers in operations research 

and finance journals such as Mathematical Programming, Mathematics of 

Operations Research, SIAM Journal on Optimization, European Journal of 

Operational Research, and Quantitative Finance. He has chaired a 

National Natural Science Foundation of China project and a sub-project 

of the National Key R&D Program of China, as well as some joint 

projects with industry.