A Review on Ambiguity in Stochastic Portfolio Optimization
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In mean-risk portfolio optimization, it is typically assumed that the assets follow a known distribution P 0, which is estimated from observed data. Aiming at an investment strategy which is robust against possible misspecification of P 0, the portfolio selection problem is solved with respect to the worst-case distribution within a Wasserstein-neighborhood of P 0. We review tractable formulations of the portfolio selection problem under model ambiguity, as it is called in the literature. For instance, it is known that high model ambiguity leads to equally-weighted portfolio diversification. However, it often happens that the marginal distributions of the assets can be estimated with high accuracy, whereas the dependence structure between the assets remains ambiguous. This leads to the problem of portfolio selection under dependence uncertainty. We show that in this case portfolio concentration becomes optimal as the uncertainty with respect to the estimated dependence structure increases. Hence, distributionally robust portfolio optimization can have two very distinct implications: Diversification on the one hand and concentration on the other hand.
KeywordsStochastic optimization Robustness Portfolio optimization Model uncertainty Dependence uncertainty
Mathematics Subject Classification (2010)90C15 91B28
Open access funding provided by University of Vienna. The authors acknowledge support by the Vienna Science and Technologie Fund (WWTF) through project MA14-008.
- 5.Bertsimas, D., Gupta, V., Kallus, N.: Robust SAA. arXiv:1408.4445, p. 617 (2014)
- 6.Brandt, M.: Portfolio choice problems. Handbook Financ. Economet. 1, 269–336 (2009). https://doi.org/10.1016/B978-0-444-50897-3.50008-0 Google Scholar
- 16.Esfahani, P.M., Kuhn, D. arXiv:1505.05116 (2015)
- 20.Föllmer, H., Schied, A.: Stochastic finance: an introduction in discrete time Walter de Gruyter (2011). https://doi.org/10.1515/9783110463453
- 22.Gao, R., Kleywegt, A.J.: Distributionally robust stochastic optimization with Wasserstein distance. arXiv:1604.02199 (2016)
- 26.Ji, R., Lejeune, M.: Data-driven optimization of ambiguous reward-risk ratio measures. Available at SSRN 2707122 (2015)Google Scholar
- 32.Lux, T., Papapantoleon, A.: Model-free bounds on value-at-risk using partial dependence information. arXiv:1610.09734 (2016)
- 34.Markowitz, H.: Portfolio selection. J. Financ. 7(1), 77–91 (1952). https://doi.org/10.1111/j.1540-6261.1952.tb01525.x Google Scholar
- 40.Pflug, G.C., Pichler, A.: Approximations for Probability Distributions and Stochastic Optimization Problems. In: Consigli, G., Dempster, M., Bertocchi, M. (eds.) Springer Handbook on Stochastic Optimization Methods in Finance and Energy, International Series in OR and Management Science, vol. 163, pp. 343–387. Springer (2011). https://doi.org/10.1007/978-1-4419-9586-5 Google Scholar
- 50.Rüschendorf, L.: Risk Bounds and Partial Dependence Information. Preprint, University of Freiburg (2016)Google Scholar
- 51.Shorack, G.R., Wellner, J.A.: Empirical processes with applications to statistics, vol. 59 Siam (2009). https://doi.org/10.1137/1.9780898719017
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