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Coherent Measures of Risk Mathematical Finance 9

Coherent Measures of Risk Mathematical Finance 9,P. Artzner,F. Delbaen,J. M. Eber,D. Heath

Coherent Measures of Risk Mathematical Finance 9   (Citations: 9)
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Published in 1999.
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    • ...++ − + = . (3) where 1,1 k θ − is the tabulated value of the corresponding elliptical percentile 1(0,1, ) Ell f and 2 () , 1/ 1/...

    Fabio Lamantiaet al. An Empirical Comparison among VaR Models and Time Rules with Elliptica...

    • ...A comprehensive treatment can be found in Artzner et al. [2] and Delbean [9]...
    • ...where 0 < fi < 1 (see Artzner et al. [2] for further details)...

    Boualem Djehicheet al. Standard approaches to asset & liability risk

    • ...Dierent authors have recently been interested in defining and constructing a coherent, in some sense, risk measure (see, for instance, Artzner et al. [ADEH] or F¨ollmer and Schied [FS1]), using a systematic axiomatic approach...
    • ...where QH is the set of all additive measures such that 8 2 H, EQ ( ) 0. The risk measure v H is then coherent 2 in the sense of Artzner et al. ([ADEH]) and its...

    Pauline Barrieuet al. Optimal Derivatives Design under Dynamic Risk Measures

    • ...The EWMA model is an IGARCH(1,1) (integrated generalized auto-regressive conditional heteroskedastic) model...
    • ...The EWMA model is an IGARCH(1,1) (integrated generalized auto-regressive conditional heteroskedastic) model...
    • ...follows a strong IGARCH(1,1), that is also a particular ISR-SARV(1) process (Integrated Square-Root Stochastic Autoregressive Volatility process i.e., () 1 0...
    • ...follows a strong IGARCH(1,1), that is also a particular ISR-SARV(1) process (Integrated Square-Root Stochastic Autoregressive Volatility process i.e., () 1 0...
    • ...follows a strong IGARCH(1,1), that is also a particular ISR-SARV(1) process (Integrated Square-Root Stochastic Autoregressive Volatility process i.e., () 1 0...
    • ...tk Tk Z + ∈` is still an ISR-SARV(1) process...
    • ...u in the high frequency IGARCH(1,1) process...
    • ...u in the high frequency IGARCH(1,1) process...
    • ...corresponding to the aggregated ISR-SARV(1) process tT Z + follows the rules explained in Meddahi and Renault, 2004...
    • ...On the other hand, the conditional variance-covariance matrix of tT Z + at time t for the EWMA model follows the rules of aggregated ISR-SARV(1) process...
    • ...to zero. If we assume the high frequency strong IGARCH(1,1) process (on the marginal distributions, or on the portfolios) 22...
    • ...to zero. If we assume the high frequency strong IGARCH(1,1) process (on the marginal distributions, or on the portfolios) 22...
    • ...In the case of strictly stationary IGARCH (1,1), portfolio VaR and CVaR for the temporal horizon T cannot be derived by the rules of aggregated conditional variance process explained in Meddahi and Renault, 2004...
    • ...In the case of strictly stationary IGARCH (1,1), portfolio VaR and CVaR for the temporal horizon T cannot be derived by the rules of aggregated conditional variance process explained in Meddahi and Renault, 2004...
    • ...As a matter of fact, even if the Gaussian IGARGH(1,1) model presents good performance at high frequency, say daily or intraday returns, the Gaussian IGARCH(1,1) is often rejected at low frequency, see Lamantia et al., 2006...
    • ...As a matter of fact, even if the Gaussian IGARGH(1,1) model presents good performance at high frequency, say daily or intraday returns, the Gaussian IGARCH(1,1) is often rejected at low frequency, see Lamantia et al., 2006...
    • ...As a matter of fact, even if the Gaussian IGARGH(1,1) model presents good performance at high frequency, say daily or intraday returns, the Gaussian IGARCH(1,1) is often rejected at low frequency, see Lamantia et al., 2006...
    • ...As a matter of fact, even if the Gaussian IGARGH(1,1) model presents good performance at high frequency, say daily or intraday returns, the Gaussian IGARCH(1,1) is often rejected at low frequency, see Lamantia et al., 2006...
    • ...Moreover, under these assumptions, the aggregated process is a particular ISR-SARV(1)...
    • ...11 (0,1, ); (0,1, ) Ell f Ell f � conditional value at risk values...
    • ...11 (0,1, ); (0,1, ) Ell f Ell f � conditional value at risk values...
    • ...distribution 1 (0,1, ) Ell f� derived from the convolution of i.i.d...
    • ...In order to fix one for any (1, 2) α ∈ , we can write...
    • ...covariance matrix. In addition, B G is also an α -stable sub-Gaussian vector where the components i ε = B i G are (1, 0, 0) Sα distributed, while the dispersion matrix V (that for simplicity we consider invertible) is obtained by the nn × matrix Σ i.e...
    • ...stable sub-Gaussian (α∈(1,2)) with characteristic function...
    • ...BG ++ are (1, 0, 0) distributed, while the entries of dispersion matrix...
    • ...Thus, the above model is a particular Stable GARCH(1,1) model (see, among others, Rachev and Mittnik, 2000) and it is also an EWMA model and an ISR-SARV(1)...
    • ...Thus, the above model is a particular Stable GARCH(1,1) model (see, among others, Rachev and Mittnik, 2000) and it is also an EWMA model and an ISR-SARV(1)...
    • ...Thus, the above model is a particular Stable GARCH(1,1) model (see, among others, Rachev and Mittnik, 2000) and it is also an EWMA model and an ISR-SARV(1)...
    • ...XS α (1, 0, 0) . Even in this case, we can consider the aggregated process...
    • ...In particular, the aggregated process is still an ISR-SARV(1) process if we consider the variance...

    Fabio Lamantiaet al. VaR, CVaR and Time Rules with Elliptical and Asymmetric Stable Distrib...

    • ...Further risk measures can be found in the class of coherent measures introduced by Artzner, Delbaen, Eber and Heath [1] and Delbaen [5]...

    Abdelali Gabihet al. Optimal portfolios with bounded Expected Loss

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