Risk Aversion in Regulatory Capital Principles

Mao, Tiantian; Wang, Ruodu

doi:10.1137/18m121842x

Cited by 48 publications

(58 citation statements)

References 34 publications

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“…Furthermore, we show that under law invariance star-shaped acceptability indexes preserve second-order dominance stochastic, linked to risk aversion. This is in connection to consistent risk measures as proposed by Mao and Wang (2020).…”

Section: Introductionsupporting

confidence: 58%

Star-shaped acceptability indexes

Righi¹

2021

Preprint

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We propose the star-shaped acceptability indexes as generalizations of both the approaches of Cherny and Madan (2009) and Rosazza Gianin and Sgarra (2013) in the same vein as star-shaped risk measures generalize both the classes of coherent and convex risk measures. We characterize acceptability indexes through star-shaped risk measures, star-shaped acceptance sets, and as the minimum of some family of quasi-concave acceptability indexes. Further, we introduce concrete examples under our approach linked to Value at Risk, riskadjusted reward on capital, reward-based gain-loss ratio, monotone reward-deviation ratio, and robust acceptability indexes. We also expose an application regarding optimization of performance.

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Section: Introductionsupporting

confidence: 58%

Star-shaped acceptability indexes

Righi¹

2021

Preprint

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“…The desired representation follows from Proposition 2 by setting

D = {α_{Y, ϵ}; Y \in scriptA, ϵ > 0}

, where

α_{Y, ϵ} false(u false) = F_{Y - ϵ} false(u false)

for

u \geq 0

. The above representation can be viewed as a first‐order dominance counterpart of the representation of “consistent risk measures” obtained in Theorem 3.1 in Mao and Wang, (). We thank Ruodu Wang for pointing this out.…”

Section: Finance Theoretical Propertiesmentioning

confidence: 96%

Risk Measures Based on Benchmark Loss Distributions

Bignozzi¹,

Burzoni²,

Munari³

2019

J of Risk & Insurance

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We introduce a class of quantile-based risk measures that generalize Value at Risk (VaR) and, likewise Expected Shortfall (ES), take into account both the frequency and the severity of losses. Under VaR a single confidence level is assigned regardless of the size of potential losses. We allow for a range of confidence levels that depend on the loss magnitude. The key ingredient is a benchmark loss distribution (BLD), that is, a function that associates to each potential loss a maximal acceptable probability of occurrence. The corresponding risk measure, called Loss VaR (LVaR), determines the minimal capital injection that is required to align the loss distribution of a risky position to the target BLD. By design, one has full flexibility in the choice of the BLD profile and, therefore, in the range of relevant quantiles. Special attention is given to piecewise constant functions and to tail distributions of benchmark random losses, in which case the acceptability condition imposed by the BLD boils down to first-order stochastic dominance. We investigate the main theoretical properties of LVaR with a focus on their comparison with VaR and ES and discuss applications to capital adequacy, portfolio risk management, and catastrophic risk.

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“…Almost all risk measures used in practice are monotone; ES is consistent with convex order whereas VaR is not. Monetary risk measures (see Föllmer and Schied (2016)) that are consistent with convex order are characterized by Mao and Wang (2020) and they admit an ES-based representation. In particular, all lower semi-continuous convex risk measures, including ES and expectiles (e.g., Ziegel (2016) and Delbaen et al (2016)), are consistent with convex order; we refer to Föllmer and Schied (2016) for an overview on risk measures.…”

Section: Inequalities Implied By Stochastic Dominancementioning

confidence: 99%

Ordering and inequalities for mixtures on risk aggregation

Chen

Liu

et al. 2021

Mathematical Finance

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Aggregation sets, which represent model uncertainty due to unknown dependence, are an important object in the study of robust risk aggregation. In this paper, we investigate ordering relations between two aggregation sets for which the sets of marginals are related by two simple operations: distribution mixtures and quantile mixtures. Intuitively, these operations "homogenize" marginal distributions by making them similar.

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Risk Aversion in Regulatory Capital Principles

Cited by 48 publications

References 34 publications

Star-shaped acceptability indexes

Star-shaped acceptability indexes

Risk Measures Based on Benchmark Loss Distributions

Ordering and inequalities for mixtures on risk aggregation

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