Abstract
In this article we focus on multistage portfolio optimization problem with usage of multivariate stochastic dominance constraints. The first part of the work is devoted to the theoretical background needed for establishing the optimization problem. We provide a general approach to multivariate stochastic dominance, we mainly recall basic definitions and several statements that are relevant for portfolio optimization, and describe an algorithm for detecting multivariate stochastic dominance of two random vectors with discrete distributions. The main part of the work introduces multivariate stochastic dominance constraints in multistage portfolio optimization problem. We compare obtained results with traditional model which employs univariate first order stochastic dominance constraints at each stage.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Armbruster B, Luedtke J (2015) Models and formulations for multivariate dominance-constrained stochastic programs. IIE Trans 47:1–14
Bruni R, Cesarone F, Scozzari A, Tardella F (2017) On exact and approximate stochastic dominance strategies for portfolio selection. Eur J Oper Res 259:322–329
Dentcheva D, Ruszczýnski A (2009) Optimization with multivariate stochastic dominance constraints. Math Program 117:111–127
Dentcheva D, Wolfhagen E (2015) Optimization with multivariate stochastic dominance constraints. SIAM J Optim 25(1):564–588
Dentcheva D, Wolfhagen E (2016) Two-stage optimization problems with multivariate stochastic order constraints. Math Oper Res 41(1):1–22
French KR (2017) 10 industry portfolios of the US stocks. http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/index.html
Guo X, Wong WK (2016) Multivariate stochastic dominance for risk averters and risk seekers, MPRA Paper, 70637
Huang CC, Vertinsky I, Ziemba WT (1978) On multiperiod stochastic dominance. J Financ Quant Anal 13:1–13
Kopa M, Moriggia V, Vitali S (2018) Individual optimal pension allocation under stochastic dominance constraints. Ann Oper Res 260(1–2):255–291
Kopa M, Petrová B (2017) Strong and weak multivariate first-order stochastic dominance, working paper, https://ssrn.com/abstract=3144058
Levhari D, Paroush J, Peleg B (1975) Efficiency analysis for multivariate distributions. Rev Econ Stud 42:87–91
Levy H (1973) Stochastic dominance, efficiency criteria and efficient portfolios: the multiperiod case. Am Econ Rev 63:986–994
Levy H (2006) Stochastic dominance: investment decision making under uncertainty. Springer, New York
Levy H, Paroush J (1974) Multi-period stochastic dominance. J Financ Quant Anal 21:428–435
Pflug G, Pichler A (2014) Multistage stochastic optimization. Springer, Berlin
Post T, Kopa M (2013) General linear formulations of stochastic dominance criteria. Eur J Oper Res 230:321–332
Post T, Kopa M (2017) Portfolio choice based on third-degree stochastic dominance. Manag Sci 63(10):3381–3392
Roman D, Mitra G, Zverovich V (2013) Enhanced indexation based on second-order stochastic dominance. Eur J Oper Res 228:273–281
Shapiro A, Dentcheva D, Ruszczýnski A (2009) Lectures on stochastic programming: modeling and theory. SIAM, Philadelphia
Sriboonchitta S, Wong WK, Dhompongsa S, Nguyen HT (2009) Stochastic dominance and applications to finance, risk and economics. Chapman and Hall/CRC, Boca Raton
Acknowledgements
I would like to express the gratitude to my supervisor Miloš Kopa for his valuable comments to this article. This work was supported by Czech Science Foundation (Grant 402/12/G097).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Petrová, B. Multistage portfolio optimization with multivariate dominance constraints. Comput Manag Sci 16, 17–46 (2019). https://doi.org/10.1007/s10287-018-0334-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10287-018-0334-9