Panjer recursion versus FFT for compound distributions

Embrechts, Paul; Frei, Mario

doi:10.1007/s00186-008-0249-2

Cited by 83 publications

(67 citation statements)

References 20 publications

(17 reference statements)

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“…The thin dashed line corresponds to the benchmark value of the required relic abundance cross section (3 × 10 −26 cm 3 /s), while the solid horizontal line corresponds to the detailed calculation of this quantity derived by Steigman et al [18]. The observed limits are below this latter curve for masses less than [0, 26, 54] GeV (for annihilation into bb), [18,29,62] GeV (τ + τ − ), [21,35,64] GeV (uū, dd, ss, cc, and gg), [87,114,146] GeV (γγ), and [5,6,10] GeV (e + e − ), where the quantities in brackets are for the −1σ, median, and +1σ levels of the systematic uncertainty band. A machine-readable file tabulating these limits is available as Supplemental Material.…”

Section: A Comment On An Apparent Excessmentioning

confidence: 88%

Comprehensive search for dark matter annihilation in dwarf galaxies

2015

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We present a new formalism designed to discover dark matter annihilation occurring in the Milky Way's dwarf galaxies. The statistical framework extracts all available information in the data by simultaneously combining observations of all the dwarf galaxies and incorporating the impact of particle physics properties, the distribution of dark matter in the dwarfs, and the detector response. The method performs maximally powerful frequentist searches and produces confidence limits on particle physics parameters. Probability distributions of test statistics under various hypotheses are constructed exactly, without relying on large sample approximations. The derived limits have proper coverage by construction and claims of detection are not biased by imperfect background modeling. We implement this formalism using data from the Fermi Gamma-ray Space Telescope to search for an annihilation signal in the complete sample of Milky Way dwarfs whose dark matter distributions can be reliably determined. We find that the observed data is consistent with background for each of the dwarf galaxies individually as well as in a joint analysis. The strongest constraints are at small dark matter particle masses. Taking the median of the systematic uncertainty in dwarf density profiles, the cross section upper limits are below the pure s-wave weak scale relic abundance value (2.2×10 −26 cm 3 s −1 ) for dark matter masses below 26 GeV (for annihilation into bb), 29 GeV (τ + τ − ), 35 GeV (uū, dd, ss, cc, and gg), 6 GeV (e + e − ), and 114 GeV (γγ). For dark matter particle masses less than 1 TeV, these represent the strongest limits obtained to date using dwarf galaxies.

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Section: A Comment On An Apparent Excessmentioning

confidence: 88%

Comprehensive search for dark matter annihilation in dwarf galaxies

2015

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“…El siguiente gráfico reproduce la figura 1 de Embrechts y Frei [21], donde se asume que las pérdidas siguen una distribución Pareto(4,3) y las frecuencias una distribución Poisson (20).…”

Section: A) Recursión De Panjerunclassified

“…El primer caso es un proceso con intensidad (tasa de llegada) constante, mientras que en el proceso de Cox la intensidad depende del tiempo, pero además es estocástica. Fuente: elaboración propia basado en [21] c) Aproximaciones…”

Section: A) Recursión De Panjerunclassified

“…Comentarios Para más detalles de los métodos de recursión y FFT como sus problemas, ver [21] y las referencias allí contenidas. Aunque el algoritmo recursivo de Panjer ha sido ampliamente usado en actuaría y presenta una aproximación confiable a la distribución de pérdidas agregadas, los autores reconocen que FFT posee dos ventajas sobre este algoritmo.…”

Section: D) Simulaciónunclassified

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Construcción de la distribución de pérdidas y el problema de agregación de riesgo operativo bajo modelos LDA: una revisión

Valencia

2013

rev.ing.univ.Medellin

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RESUMENEste artículo revisa la literatura más reciente en cuanto a la obtención de la distribución de pérdidas para riesgo operativo cuando se emplea el modelo de distribución de pérdidas agregadas (LDA, por sus siglas en inglés), y dependencia entre las líneas operativas. Cuando LDA es el método escogido para cuantificar riesgo operativo existen algunas cuestiones a resolver. Entre ellas está la obtención de la distribución de pérdidas, puesto que no existe una fórmula cerrada para obtenerla; sin embargo, existen métodos numéricos para resolver este problema. Finalmente, se presenta una revisión en cuanto a la obtención del riesgo operativo total de una entidad financiera, teniendo en cuenta la dependencia existente entre las diferentes líneas operativas.Palabras clave: enfoque de distribución de pérdidas agregadas, valor en riesgo, agregación, cópulas.

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“…In some rare cases, it is possible to write the integral in (5.14) in closed form. For general marginals, one can for instance rely on the Fast Fourier Transforms; see [8] and the references therein for a discussion within a risk management context.…”

Section: The Calculation Of the Distribution Of The Sum Of Risksmentioning

confidence: 99%

Risk Aggregation

Embrechts

Puccetti

2010

Copula Theory and Its Applications

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Quantitative Risk Management (QRM) often starts with a vector of oneperiod profit-and-loss random variables X = (X 1 , . . . , X d ) ′ defined on some probability space (Ω , F, P). Risk Aggregation concerns the study of the aggregate financial position Ψ (X), for some measurable function Ψ : R d → R. A risk measure ρ then maps Ψ (X) to ρ(Ψ(X)) ∈ R, to be interpreted as the regulatory capital needed to be able to hold the aggregate position Ψ (X) over a predetermined fixed time period. Risk Aggregation has often been studied within the framework when only the marginal distributions F 1 , . . . , F d of the individual risks X 1 , . . . , X d are available. Recently, especially in the management of operational risk, cases in which further dependence information is available have become relevant. We introduce a general mathematical framework which interpolates between marginal knowledge (F 1 , . . . , F d ) and full knowledge of F X , the distribution of X. We illustrate the basic issues through some pedagogic examples of actuarial and financial interest. In particular, we study Risk Aggregation under different mathematical set-ups, for different aggregating functionals Ψ and risk measures ρ, focusing on Value-at-Risk. We show how the theory of Mass Transportations and tools originally developed to solve so-called Monge-Kantorovich problems turn out to be useful in this context. Finally, we introduce some new numerical integration techniques which solve some open aggregation problems and raise new interesting research issues.

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Panjer recursion versus FFT for compound distributions

Cited by 83 publications

References 20 publications

Comprehensive search for dark matter annihilation in dwarf galaxies

Comprehensive search for dark matter annihilation in dwarf galaxies

Construcción de la distribución de pérdidas y el problema de agregación de riesgo operativo bajo modelos LDA: una revisión

Risk Aggregation

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