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Optimal Portfolios Under Worst-Case Scenarios

Forthcoming in Quantitative Finance

32 Pages Posted: 4 Nov 2013  

Carole Bernard

Grenoble Ecole de Management

Jit Seng Chen


Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Date Written: January 1, 2012


In standard portfolio theories such as Mean-Variance optimization, Expected Utility Theory, Rank Dependent Utility Theory, Yaari’s Dual Theory and Cumulative Prospect Theory, the worst outcomes for optimal strategies occur when the market declines (e.g, during crises), which is at odds with the needs of many investors. Hence, we depart from the traditional settings and study optimal strategies for investors who impose additional constraints on their final wealth in the states corresponding to a stressed financial market. We provide a framework that maintains the stylized features of the SP/A theory while dealing with the goal of security in a more flexible way. Preferences become state-dependent, and we assess the impact of these preferences on trading decisions. We construct optimal strategies explicitly and show how they outperform traditional diversified strategies under worst-case scenarios.

Keywords: Behavioral Portfolio Selection, State-dependent preferences, Risk Diversification, Cost-efficiency, Path-dependent Strategies, Growth Optimal Portfolio

Suggested Citation

Bernard, Carole and Chen, Jit Seng and Vanduffel, Steven, Optimal Portfolios Under Worst-Case Scenarios (January 1, 2012). Forthcoming in Quantitative Finance. Available at SSRN: or

Carole Bernard

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003

Jit Seng Chen

Independent ( email )

No Address Available

Steven Vanduffel (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050


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