Skip to main content

Please enter a keyword and click the arrow to search the site

Robust portfolio choice with learning in the framework of regret: Single period case

Journal

Management Science

Subject

Management Science and Operations

Authors / Editors

Lim A E B;Shanthikumar J G;Ban G-Y

Publication Year

2012

Abstract

In this paper, we formulate a single-period portfolio choice problem with parameter uncertainty in the framework of relative regret. Relative regret evaluates a portfolio by comparing its return to a family of benchmarks, where the benchmarks are the wealths of fictitious investors who invest optimally given knowledge of the model parameters, and is a natural objective when there is concern about parameter uncertainty or model ambiguity. The optimal relative regret portfolio is the one that performs well in relation to all the benchmarks over the family of possible parameter values. We analyze this problem using convex duality and show that it is equivalent to a Bayesian problem, where the Lagrange multipliers play the role of the prior distribution, and the learning model involves Bayesian updating of these Lagrange multipliers/prior. This Bayesian problem is unusual in that the prior distribution is endogenously chosen by solving the dual optimization problem for the Lagrange multipliers, and the objective function involves the family of benchmarks from the relative regret problem. These results show that regret is a natural means by which robust decision making and learning can be combined.

Keywords

Parameter uncertainty; Ambiguity; Model uncertainty; Learning; Regret; Relative regret; Competitive analysis; Portfolio selection; Bayesian methods; Objective-based loss functions; Convex duality

Available on ECCH

No


Select up to 4 programmes to compare

Select one more to compare
×
subscribe_image_desktop 5949B9BFE33243D782D1C7A17E3345D0

Sign up to receive our latest news and business thinking direct to your inbox

×

Sign up to receive our latest course information and business thinking

Leave your details above if you would like to receive emails containing the latest thought leadership, invitations to events and news about courses that could enhance your career. If you would prefer not to receive our emails, you can still access the case study by clicking the button below. You can opt-out of receiving our emails at any time by visiting: https://london.edu/my-profile-preferences or by unsubscribing through the link provided in our emails. View our Privacy Policy for more information on your rights.