Expected Shortfall and Beyond

Tasche, Dirk

doi:10.1007/978-3-0348-8201-9_9

Cited by 74 publications

(84 citation statements)

References 21 publications

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“…It is not a subadditive measure of risk (see Section...) which means that the risk of a portfolio can be larger than the sum of the stand-alone risks of its components when measured by VaR -see [4] for more details and see [48] for examples showing the lack of subadditivity of VaR. In addition, VaR is not convex with respect to choice x, thus it is difficult to optimise with standard available methods ( [20], [23] and references therein).…”

Section: Remark 3 Although the Calculation Of V Ar α Indicates That Wmentioning

confidence: 99%

Portfolio selection models: a review and new directions

Roman

Mitra

2009

Wilmott Journal

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Modern Portfolio Theory (MPT) is based upon the classical Markowitz model which uses variance as a risk measure. A generalization of this approach leads to mean‐risk models, in which a return distribution is characterized by the expected value of return (desired to be large) and a “risk” value (desired to be kept small). Portfolio choice is made by solving an optimization problem, in which the portfolio risk is minimized and a desired level of expected return is specified as a constraint. The need to penalize different undesirable aspects of the return distribution led to the proposal of alternative risk measures, notably those penalizing only the downside part (adverse) and not the upside (potential). The downside risk considerations constitute the basis of the Post Modern Portfolio Theory (PMPT). Examples of such risk measures are lower partial moments, Value‐at‐Risk (VaR) and Conditional Value‐at‐Risk (CVaR). We revisit these risk measures and the resulting mean‐risk models. We discuss alternative models for portfolio selection, their choice criteria and the evolution of MPT to PMPT which incorporates: utility maximization and stochastic dominance. Copyright © 2009 Wilmott Magazine Ltd

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Section: Remark 3 Although the Calculation Of V Ar α Indicates That Wmentioning

confidence: 99%

Portfolio selection models: a review and new directions

Roman

Mitra

2009

Wilmott Journal

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“…Since then, the theory of coherent risk measures has rapidly been evolving; it already occupies a considerable part of the modern financial mathematics. Let us cite the papers [1], [2], [3], [6], [16], [19], [24], [27], [28], [30], [36], [41], [43], [52], [61], to mention only a few. Nice reviews on the theory of coherent risk measures are given in [20], [29;Ch.…”

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confidence: 99%

Coherent Measurement of Factor Risks

Cherny

Madan

2006

SSRN Journal

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Abstract. We propose a new procedure for the risk measurement of large portfolios. It employs the following objects as the building blocks:• coherent risk measures introduced by Artzner, Delbaen, Eber, and Heath;• factor risk measures introduced in this paper, which assess the risks driven by particular factors like the price of oil, S&P500 index, or the credit spread; • risk contributions and factor risk contributions, which provide a coherent alternative to the sensitivity coefficients. We also propose two particular classes of coherent risk measures called Alpha V@R and Beta V@R, for which all the objects described above admit an extremely simple empirical estimation procedure. This procedure uses no model assumptions on the structure of the price evolution.Moreover, we consider the problem of the risk management on a firm's level. It is shown that if the risk limits are imposed on the risk contributions of the desks to the overall risk of the firm (rather than on their outstanding risks) and the desks are allowed to trade these limits within a firm, then the desks automatically find the globally optimal portfolio.

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“…Alternative risk measures to VaR have been proposed in the literature, from which Expected shortfall (ES) is the most discussed. For a discussion regarding the advantage of this risk measure over VaR we refer the reader to Tasche (2002).…”

Section: Risk Measuresmentioning

confidence: 99%

Extremes on the discounted aggregate claims in a time dependent risk model

Asimit

Badescu

2010

Scandinavian Actuarial Journal

115

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This paper presents an extension of the classical compound Poisson risk model for which the inter-claim time and the forthcoming claim amount are no longer independent random variables. Asymptotic tail probabilities for the discounted aggregate claims are presented when the force of interest is constant and the claim amounts are heavy tail distributed random variables. Furthermore, we derive asymptotic finite time ruin probabilities, as well as asymptotic approximations for some common risk measures associated with the discounted aggregate claims.A simulation study is performed in order to validate the results obtained in the free interest risk model.

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Expected Shortfall and Beyond

Cited by 74 publications

References 21 publications

Portfolio selection models: a review and new directions

Portfolio selection models: a review and new directions

Coherent Measurement of Factor Risks

Extremes on the discounted aggregate claims in a time dependent risk model

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