Certainty equivalent measures of risk

Vinel, Alexander; Krokhmal, Pavlo A.

doi:10.1007/s10479-015-1801-0

Cited by 19 publications

(18 citation statements)

References 27 publications

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“…Then, CE X = v −1 E v X represents the CE of loss X, i.e., such a deterministic loss that a rational decision maker with deutility function v would be indifferent between CE X and stochastic loss profile X. The following argument can be used to construct risk measures of the form (2) that employ rational utility maximizer's preferences via CEs (Vinel and Krokhmal 2014a, see also Ben-Tal and Teboulle 2007). Consider a decision maker who faces an uncertain future loss X, but who can allocate an amount of resources now to cover the future loss.…”

Section: A Class Of Downside Riskmentioning

confidence: 99%

“…When p > 1, HMCR measures quantify risk via higher tail moments X − + p , and have been shown to be better suited for applications that involve heavy-tailed loss distributions (Krokhmal 2007). Likewise, the Log Exp CR family (6) is designed for dealing with heavy-tailed distributions; moreover, in addition to being SSD isotonic, Log Exp CR measures are isotonic regarding stochastic dominance of arbitrary order (k SD), see Vinel and Krokhmal (2014a).…”

Section: A Class Of Downside Riskmentioning

confidence: 99%

“…As an illustrative example of the general approach, we consider stochastic optimization problems with higher-moment coherent risk (HMCR) measures, which quantify risk via higher moments of cost or loss distributions (Krokhmal 2007), making them advantageous in the presence of "heavy-tailed" uncertainty. We also apply the proposed method to problems with log-exponential convex risk (LogExpCR) measures (Vinel and Krokhmal 2014a).…”

Section: Introductionmentioning

confidence: 99%

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A Scenario Decomposition Algorithm for Stochastic Programming Problems with a Class of Downside Risk Measures

Rysz

Vinel

Krokhmal

et al. 2015

INFORMS Journal on Computing

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W e present an efficient scenario decomposition algorithm for solving large-scale convex stochastic programming problems that involve a particular class of downside risk measures. The considered risk functionals encompass coherent and convex measures of risk that can be represented as an infimal convolution of a convex certainty equivalent, and include well-known measures, such as conditional value-at-risk, as special cases. The resulting structure of the feasible set is then exploited via iterative solving of relaxed problems, and it is shown that the number of iterations is bounded by a parameter that depends on the problem size. The computational performance of the developed scenario decomposition method is illustrated on portfolio optimization problems involving two families of nonlinear measures of risk, the higher-moment coherent risk measures, and log-exponential convex risk measures. It is demonstrated that for large-scale nonlinear problems the proposed approach can provide up to an order-of-magnitude improvement in computational time in comparison to state-of-the-art solvers, such as CPLEX, Gurobi, and MOSEK.

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Section: A Class Of Downside Riskmentioning

confidence: 99%

Section: A Class Of Downside Riskmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Scenario Decomposition Algorithm for Stochastic Programming Problems with a Class of Downside Risk Measures

Rysz

Vinel

Krokhmal

et al. 2015

INFORMS Journal on Computing

Self Cite

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“…With additional assumptions (see, for example, [ 4 ]), there exists a one-to-one pairing between

and

via Legendre-Fenchel (LF) duality. The theories of convex and coherent risk measures have been increasingly and deeply developed as a central axis of the general theory of measures of risk, owing to the contributions by many researchers (e.g., [ 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ], etc; see also early work of [ 13 ], among others). In the law-invariant case [ 14 ], the value

only depends on the distribution of

under the assumption of a prefixed probability measure P on

.…”

Section: Introductionmentioning

confidence: 99%

Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions

Angulo

2019

Entropy

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This paper introduces a new family of the convex divergence-based risk measure by specifying ( h , ϕ ) -divergence, corresponding with the dual representation. First, the sensitivity characteristics of the modified divergence risk measure with respect to profit and loss (P&L) and the reference probability in the penalty term are discussed, in view of the certainty equivalent and robust statistics. Secondly, a similar sensitivity property of ( h , ϕ ) -divergence risk measure with respect to P&L is shown, and boundedness by the analytic risk measure is proved. Numerical studies designed for Rényi- and Tsallis-divergence risk measure are provided. This new family integrates a wide spectrum of divergence risk measures and relates to divergence preferences.

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“…Related to this premium, one could consider just the expected value and compute the expected disutility (Borch 1961 [2]) obtaining π(F ) = E(V (X)). (9) For generalizations of the CEQ premium see Vinel and Krokhmal 2017 [24]. The ambiguity principle.…”

Section: Introductionmentioning

confidence: 99%

The distortion principle for insurance pricing: properties, identification and robustness

Escobar

Pflug

2018

Ann Oper Res

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Distortion (Denneberg 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein distance. We study variances of distances for probability models and identify some worst case distributions. In addition to the direct problem we also investigate the inverse problem, that is how to identify the distortion density on the basis of observations of insurance premia.

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Certainty equivalent measures of risk

Cited by 19 publications

References 27 publications

A Scenario Decomposition Algorithm for Stochastic Programming Problems with a Class of Downside Risk Measures

A Scenario Decomposition Algorithm for Stochastic Programming Problems with a Class of Downside Risk Measures

Divergence-Based Risk Measures: A Discussion on Sensitivities and Extensions

The distortion principle for insurance pricing: properties, identification and robustness

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