Shortfall Risk Models When Information on Loss Function Is Incomplete

Delage, Erick; Guo, Shaoyan; Xu, Huifu

doi:10.1287/opre.2021.2212

Cited by 16 publications

(11 citation statements)

References 12 publications

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“…The certainty equivalent approach is well‐known in the literature of PRO, see Delage et al. (2022) and references therein.…”

Section: Ambiguity Set Of the Distortion Functionsmentioning

confidence: 99%

“…To analyze how sensitive the distortion function is to a small probability, we consider the following class of distortion functions based on Delage et al. (2022).…”

Section: Ambiguity Set Of the Distortion Functionsmentioning

confidence: 99%

“…Delage et al. (2022) consider a PRO model for shortfall risk measures where the ambiguity set of convex loss functions is characterized using risk preference information such as certainty equivalent and sensitivity to tail events and give the tractable reformulations for the minimax optimization problem when the underlying random loss is discretely distributed. More recently, Wang and Xu (2020) consider a PRO model for decision‐making problems where the DM's risk preference is ambiguous and can be characterized via a risk spectrum.…”

Section: Introductionmentioning

confidence: 99%

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Preference robust distortion risk measure and its application

Wang

2023

Mathematical Finance

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Distortion risk measure (DRM) plays a crucial role in management science and finance particularly actuarial science. Various DRMs have been introduced but little is discussed on which DRM at hand should be chosen to address a decision maker's (DM's) risk preference. This paper aims to fill out the gap. Specifically, we consider a situation where the true distortion function is unknown either because it is difficult to identify/elicit and/or because the DM's risk preference is ambiguous. We introduce a preference robust distortion risk measure (PRDRM), which is based on the worst-case distortion function from an ambiguity set of distortion functions to mitigate the impact arising from the ambiguity. The ambiguity set is constructed under well-known general principles such as concavity and inverse S-shapedness of distortion functions (overweighting on events from impossible to possible or possible to certainty and underweighting on those from possible to more possible) as well as new user-specific information such as sensitivity to tail losses, confidence intervals to some lotteries, and preferences to certain lotteries over others. To calculate the proposed PRDRM, we use the convex and/or concave envelope of a set of points to characterize the curvature This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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“…The certainty equivalent approach is well‐known in the literature of PRO, see Delage et al. (2022) and references therein.…”

Section: Ambiguity Set Of the Distortion Functionsmentioning

confidence: 99%

“…To analyze how sensitive the distortion function is to a small probability, we consider the following class of distortion functions based on Delage et al. (2022).…”

Section: Ambiguity Set Of the Distortion Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Preference robust distortion risk measure and its application

Wang

2023

Mathematical Finance

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“…Armbruster and Delage [7] also consider the case that the derivative of the utility function exists and is convex to capture risk prudence, i.e., the decision maker is more risk tolerant when the cost is lower. For an ambiguous risk minimization problem and given certain properties such as coherence and convexity on the risk measure, Delage et al [107] derive an equivalent shortfall risk minimization problem where the utility function lies in an ambiguity set.…”

Section: Utility Functionmentioning

confidence: 99%

Frameworks and Results in Distributionally Robust Optimization

Rahimian¹,

Mehrotra²

2022

Open Journal of Mathematical Optimization

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The concepts of risk aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. The statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. This paper surveys main concepts and contributions to DRO, and relationships with robust optimization, risk aversion, chance-constrained optimization, and function regularization. Various approaches to model the distributional ambiguity and their calibrations are discussed. The paper also describes the main solution techniques used to the solve the resulting optimization problems.

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“…Hu and Stepanyan [25] propose a so-called reference-based almost stochastic dominance method for constructing a set of utility functions near a reference utility which satisfies certain stochastic dominance relationship and use the set to characterize the decision maker's preference. Over the past few years, the research on PRO has received increasing attentions in the communities of stochastic/robust optimization and risk management, see for instances [22,21,14,52,31,32] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Preference Robust Modified Optimized Certainty Equivalent

Wu¹,

Xu²

2022

Preprint

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Ben-Tal and Teboulle [6] introduce the concept of optimized certainty equivalent (OCE) of an uncertain outcome as the maximum present value of a combination of the cash to be taken out from the uncertain income at present and the expected utility value of the remaining uncertain income. In this paper, we consider two variations of the OCE. First, we introduce a modified OCE by maximizing the combination of the utility of the cash and the expected utility of the remaining uncertain income so that the combined quantity is in a unified utility value. Second, we consider a situation where the true utility function is unknown but it is possible to use partially available information to construct a set of plausible utility functions. To mitigate the risk arising from the ambiguity, we introduce a robust model where the modified OCE is based on the worst-case utility function from the ambiguity set. In the case when the ambiguity set of utility functions is constructed by a Kantorovich ball centered at a nominal utility function, we show how the modified OCE and the corresponding worst case utility function can be identified by solving two linear programs alternatively. We also show the robust modified OCE is statistically robust in a data-driven environment where the underlying data are potentially contaminated. Some preliminary numerical results are reported to demonstrate the performance of the modified OCE and the robust modified OCE model.

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Shortfall Risk Models When Information on Loss Function Is Incomplete

Cited by 16 publications

References 12 publications

Preference robust distortion risk measure and its application

Preference robust distortion risk measure and its application

Frameworks and Results in Distributionally Robust Optimization

Preference Robust Modified Optimized Certainty Equivalent

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