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Statistics of Multivariate Extremes with Applications in Risk Management

von Dr. Rodrigo Herrera

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[1.] Rh/Fragment 011 07 - Diskussion
Zuletzt bearbeitet: 2014-01-07 00:15:48 Schumann
Embrechts et al. 1999b, Fragment, Gesichtet, KomplettPlagiat, Rh, SMWFragment, Schutzlevel sysop

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Untersuchte Arbeit:
Seite: 11, Zeilen: 7-10
Quelle: Embrechts et al. 1999b
Seite(n): 30, Zeilen: 5-10
The financial industry, including banking and insurance, is undergoing major changes. An increasing complexity of financial instruments calls for sophisticated risk management tools. Extreme value theory plays an important methodological role within risk management for insurance, reinsurance, and finance. The financial industry, including banking and insurance, is undergoing major changes. [...] An increasing complexity of financial instruments calls for sophisticated risk management tools. [...] Extreme value theory plays an important methodological role within risk management for insurance, reinsurance, and finance.
Anmerkungen

Wörtliche Übernahme mit Auslassung von zwei Sätzen. Ohne Quellenangabe.

Sichter
KnallErbse

[2.] Rh/Fragment 011 10 - Diskussion
Zuletzt bearbeitet: 2012-07-30 23:19:06 Hindemith
Fragment, Gesichtet, Gonzalo Olmo 2004, Rh, SMWFragment, Schutzlevel sysop, Verschleierung

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Seite: 11, Zeilen: 10-19
Quelle: Gonzalo_Olmo_2004
Seite(n): 349, 350, Zeilen: 20-27, 1-5
The question one try to answer is: If things go wrong, how wrong can they go? The variance used as a risk measure is unable to answer this question. Alternative measures regarding possible values out of the range of available information need to be defined and calculated. Extreme value theory (EVT) provides the tools to model the asymptotic distribution of the maximum of a sequence of random variables Xi, and in this sense this theory can be very helpful in order to get a first impression about how wrong things can go. A deeper insight into EVT allows knowing not only the order of convergence of the maximum but also the limiting distribution of the largest observations of the sequence. These observations are the main ingredients of more informative risk measures that are normally utilized, like Value at Risk (VaR) or Expected Shortfall. The question one would like to answer is: ‘‘If things go wrong, how wrong can they go?’’ The variance used as a risk measure is unable to answer this question.

Alternative measures regarding possible values out of the range of available information need to be defined and calculated. Extreme value theory (EVT) provides the tools to model the asymptotic distribution of the maximum of a sequence of random variables {Xn}, and in this sense this theory can be very helpful in order to obtain a first impression about how wrong things

[page 350]

can go. A deeper insight into EVT allows us to know not only the order of convergence of the maximum, but also the limiting distribution of the largest observations of the sequence. These observations are the main ingredients of more informative risk measures that have been recently introduced, like value at risk (VaR) or expected shortfall.

Anmerkungen

Source is not given. Minimally adjusted.

Sichter
(Hindemith), KnallErbse

[3.] Rh/Fragment 011 20 - Diskussion
Zuletzt bearbeitet: 2012-07-31 15:18:41 WiseWoman
Fragment, Gesichtet, Morales 2005, Rh, SMWFragment, Schutzlevel sysop, Verschleierung

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Seite: 11, Zeilen: 20-26
Quelle: Morales_2005
Seite(n): 7, Zeilen: 3-13
In this section we review the basic background for univariate and multivariate extreme value theory for iid random variables, as well as the corresponding theory for stationary processes. There is a rich literature on extreme value theory that goes back to the 1920s. Recent introductory books for the univariate case on the subject are Coles (2001), which emphasizes statistical modelling, and Embrechts et al. (1997), which is a comprehensive reference for the theory and its applications to insurance and finance. Leadbetter et al. (1983) is mostly concerned with extremes of stationary processes. In this Chapter we review the basic background for univariate and multivariate extreme value theory for iid random variables, as well as the corresponding theory for stationary processes.

There is a rich literature on extreme value theory that goes back to the 1920’s. Recent introductory books on the subject are Coles (2001), which emphasizes statistical modeling,[...] Embrechts, Klüppelberg and Mikosch (1997) is a comprehensive reference for the theory and its applications to insurance and finance. [...] Leadbetter, Lindgren and Rootzén (1983) is mostly concerned with extremes of stationary processes.

Anmerkungen

The literature review is taken from the source, shortening it slightly.

Sichter
(Hindemith), KnallErbse

[4.] Rh/Fragment 011 27 - Diskussion
Zuletzt bearbeitet: 2012-07-31 15:43:37 WiseWoman
Fougères 2004, Fragment, Gesichtet, KomplettPlagiat, Rh, SMWFragment, Schutzlevel sysop

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Untersuchte Arbeit:
Seite: 11, Zeilen: 27-28
Quelle: Fougères 2004
Seite(n): 1, Zeilen: 26-27
Useful representations in terms of maxstable distributions, regular variation functions, or point processes, have been established. Useful representations in terms of maxstable distributions, regular variation functions, or point processes, have been established.
Anmerkungen

Ohne Quellenangabe

Sichter
KnallErbse


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