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  "Title": "Tools for Quantitative Risk Management",
  "Description": "Functions and data sets for reproducing selected results\nfrom the book \"Quantitative Risk Management: Concepts,\nTechniques and Tools\". Furthermore, new developments and\nauxiliary functions for Quantitative Risk Management practice.",
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        "conditioning"
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      "author": "Marius Hofert",
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        "1 Simulate (-log-return) data $(X_t)$ from an ARMA-GARCH process",
        "2 Fit an ARMA-GARCH model to the (simulated) data",
        "3 Calculate the VaR time series",
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      "author": "Marius Hofert",
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      "headings": [
        "1 Homogeneous case",
        "1.1 Checks for method = \"dual\"",
        "1.2 Checks for method = \"Wang\"/\"Wang.Par\"",
        "1.2.1 Check of auxiliary functions with numerical integration (for $\\theta = 2$)",
        "1.2.2 Check of $h(c)$ without numerical integration (for a range of $\\theta$)",
        "1.3 Compute best/worst $\\mathrm{VaR}_\\alpha$ (via \"Wang.Par\")",
        "1.4 Comparison between various methods for computing worst value-at-risk",
        "2 Inhomogeneous case",
        "2.1 A motivation for (column) rearrangements",
        "2.2 Run-time comparison (straightforward vs efficient implementation)",
        "2.3 How rearrange() acts on specific matrices",
        "2.4 Convergence",
        "2.5 A real data application",
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