Optimization of Convex Risk Functions

By Andrzej Ruszczynski, Alexander Shapiro. Mathematics of Operations Research, 2006

590 citations recorded by the source corpus.

Subfields: Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/9e12dddecf745401f5ead2a274359135a88a0303

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In Management Science and Operations Research

Citations in the corpus

Dual characterization of properties of risk measures on Orlicz hearts (2008, unknown): “Risk measures for unbounded random variables have, among others, been studied in Frittelli and Rosazza Gianin [19,20], Delbaen [11,12], Cherny [7], Rockafellar et al. [27], Ruszczy´ nski and Shapiro [ 28 ], Filipovi´ c and Kupper [14], Cheridito and Li [6], Filipovi´ c and Svindland [15].”
Conditional Risk Mappings (2006, methodology): “In Ruszczy´ nski and Shapiro [ 17 ] a general duality framework has been developed that allows us to view earlier representation theorems for risk measures as special cases of the theory of conjugate duality in paired topological vector spaces.”
Properties of Distortion Risk Measures (2009, background): “Applications of the risk measures to portfolio optimization can be found in Rockafellar and Uryasev (2000) for CVaRα , Ruszczynski and Shapiro (2006) for convex risk measures, Acerbi and Simonetti (2002) for spectral risk measures and Rockafellar et al. (2006b) for deviation risk measures.”
A unified framework for stochastic optimization (2019, background): “This work builds on the eminal work in Ruszczy ́nski and Shapiro (2006) , which in turn uilds on what is now an extensive literature on risk measures n finance ( Rockafellar & Uryasev, 20 0 0; Kupper & Schachermayer, 0 09; Rockafellar & Uryasev, 20 02 for some key articles), with a eneral…”
Recent progress in random metric theory and its applications to conditional risk measures (2010, background): “Since the model space is too narrow to include the important risk models such as normally or log-normally distributed random variables, there is a growing mathematical flnance literature dealing with convex risk measures beyond L 1 , see e.g., [3,8,9,17,53,55, 61 ].”
Length scale and manufacturability in density-based topology optimization (2016, background): “The main difficulties with such a reformulation is the selection of the parameter κ and the fact that such an objective is not a coherent risk measure [120], i.”
On Complexity of Stochastic Programming Problems (2005, background): “In different frameworks this dual representation was derived in [1, 20, 33, 34].”
Statistical estimation of composite risk functionals and risk optimization problems (2015, background): “The currently accepted definition of a coherent risk measure was introduced in Artzner et al. (1999) for finite probability spaces and was further extended to more general spaces in Ruszczyński and Shapiro (2006), Föllmer and Schied (2011).”
Lectures on Stochastic Programming: Modeling and Theory (2009, methodology): “Our presentation is based on Ruszczyński and Shapiro [224, 226].”
Policy Gradients Beyond Expectations: Conditional Value-at-Risk (2014, background): “In other domains, the CVaR is gaining popularity due to its intuitive notion of risk on the one hand, and favorable mathematical properties on the other (Rockafellar & Uryasev, 2000; Ruszczyński & Shapiro, 2006).”
The natural Banach space for version independent risk measures (2013, background): “The proof is contained in [23] and in [24], Proposition 6.”
An enhanced model for portfolio choice with SSD criteria: a constructive approach (2011, methodology): “We solve the portfolio optimisation problem in the form (27).”
Entropic Value-at-Risk: A New Coherent Risk Measure (2012, background): “See [8] for more technical details.”