Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

Meskarian, Rudabeh; Fliege, Jörg; Xu, Huifu

doi:10.1007/s00245-014-9236-6

Cited by 7 publications

(2 citation statements)

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“…Roman et al (2006) consider the problem of constructing a portfolio with respect to SSD and propose a reference distribution of return outcomes that would be desirable under various scenarios. Inspired by the successful applications of the stochastic optimization with SSD model in portfolio optimization, Meskarian et al (2014) examine new numerical methods for a general SSD model where the underlying functions are not necessarily linear and show that the portfolio optimization problem with SSD constraints performs better than the Markowitz model. Kopa and Post (2015) propose a linear programming test to find a given investment portfolio with most desired return given specified risk tolerance over all possible portfolios using SSD criterion.…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal diversification, stochastic dominance, and sampling error

Mroua

Abid

Wong

2017

AJB

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This paper analyses the impact of sampling errors on optimal portfolio returns and investigates the optimal choice between the international and domestic diversification strategies from viewpoint of a risk-averse American investor. The study's methodology combines portfolio re-sampling, stochastic portfolio optimization with second-order stochastic dominance constraints, and nonparametric stochastic dominance testing based on subsampling simulated p-values. First, we find that reducing sampling error increases the dominance relationships between different portfolios, which, in turn, alters portfolio investment decisions. Though international diversification is preferred in some cases, the study's results show that for risk-averse US investors, in general, there is no difference between the diversification strategies; this implies that there is no increase in the expected utility of international diversification for the period before and after the 2007-2008 financial crisis. Nevertheless, we find that, stochastic diversification in domestic, global, and Europe, Australasia and Far East (EAFE) markets delivers better risk-returns for the U.S. risk averters during the crisis period.

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Section: Literature Reviewmentioning

confidence: 99%

Optimal diversification, stochastic dominance, and sampling error

Mroua

Abid

Wong

2017

AJB

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“…It might be interesting to extend the proposed penalty schemes and algorithms to the stochastic problem with multivariate dominance constraints when the random variables in the problem have finite support sets, we will do this in our follow-up work [15]. Another interesting extension will be to develop similar schemes and algorithms of second order dominance programs with continuous distributions although we may apply them to the sample average approximated problems [9,23].…”

Section: St E[(η − G(x ξ(ω)))mentioning

confidence: 99%

Exact Penalization, Level Function Method, and Modified Cutting-Plane Method for Stochastic Programs with Second Order Stochastic Dominance Constraints

Sun¹,

Xu²,

Meskarian³

et al. 2013

SIAM J. Optim.

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). Exact penalization, level function method, and modified cutting-plane method for stochastic programs with second order stochastic dominance constraints. SIAM Journal on Optimization (SIOPT), 23(1), pp. 602-631. doi: 10.1137/110850815 This is the unspecified version of the paper.This version of the publication may differ from the final published version. Abstract. Level function methods and cutting plane methods have been recently proposed to solve stochastic programs with stochastic second order dominance (SSD) constraints. A level function method requires an exact penalization setup because it can only be applied to the objective function, not the constraints. Slater constraint qualification (SCQ) is often needed for deriving exact penalization. It is well known that SSD usually does not satisfy SCQ and various relaxation schemes have been proposed so that the relaxed problem satisfies the SCQ. In this paper, we show that under some moderate conditions the desired constraint qualification can be guaranteed through some appropriate reformulation of the constraints rather than relaxation. Exact penalization schemes based on L 1 -norm and L∞-norm are subsequently derived through Robinson's error bound on convex system and Clarke's exact penalty function theorem. Moreover, we propose a modified cutting plane method which constructs a cutting plane through the maximum of the reformulated constraint functions. In comparison with the existing cutting plane methods, it is numerically more efficient because only a single cutting plane is constructed and added at each iteration. We have carried out a number of numerical experiments and the results show that our methods display better performances particularly in the case when the underlying functions are nonlinear w.r.t. decision variables. In their pioneering work [4], Dentcheva and Ruszczyński introduced a stochastic programming model with second order stochastic dominance constraints : Permanent

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