Portfolio Optimization with Risk Control by Stochastic Dominance Constraints

Darinka Dentcheva and Andrzej Ruszczyński ()
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Andrzej Ruszczyński: Rutgers University

Chapter Chapter 9 in Stochastic Programming, 2010, pp 189-211 from Springer

Abstract: Abstract For the problem of constructing a portfolio of finitely many assets whose return rates are described by a discrete joint distribution, we discuss an approach based on stochastic dominance. The portfolio return rate in this model is required to stochastically dominate a random benchmark, such as an index, or reference portfolio return. We formulate optimality conditions and duality relations for these models and construct equivalent optimization models with utility functions and law invariant coherent measures of risk. Two different formulations of the stochastic dominance constraint–primal and inverse–lead to two dual problems which involve von Neuman–Morgenstern utility functions for the primal formulation and rank dependent (or dual) utility functions for the inverse formulation. We also analyze relations of this approach to value at risk and conditional value at risk. Numerical illustration is provided.

Keywords: Utility Function; Return Rate; Stochastic Dominance; Portfolio Optimization Problem; Benchmark Portfolio (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-1-4419-1642-6_9

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DOI: 10.1007/978-1-4419-1642-6_9

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