A Bivariate Shot Noise Hawkes Process for Insurance

Abstract The Poisson process is an essential building block to move up to complicated counting processes, such as the Cox (“doubly stochastic Poisson”) process, the Hawkes (“self-exciting”) process, exponentially decaying shot-noise Poisson (simply “shot-noise Poisson”) process and the dynamic contagion process. The Cox process provides flexibility by letting the intensity not only depending on time but also allowing it to be a stochastic process. The Hawkes process has self-exciting property and clustering effects. Shot-noise Poisson process is an extension of the Poisson process, where it is capable of displaying the frequency, magnitude and time period needed to determine the effect of points. The dynamic contagion process is a point process, where its intensity generalises the Hawkes process and Cox process with exponentially decaying shot-noise intensity. To facilitate the usage of these processes in practice, we revisit the distributional properties of the Poisson, Cox, Hawkes, shot-noise Poisson and dynamic contagion process and their compound processes. We provide simulation algorithms for these processes, which would be useful to statistical analysis, further business applications and research. As an application of the compound processes, numerical comparisons of value-at-risk and tail conditional expectation are made.

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Population viewpoint on Hawkes processes

Advances in Applied Probability ◽

10.1017/apr.2016.10 ◽

2016 ◽

Vol 48 (2) ◽

pp. 463-480 ◽

Cited By ~ 7

Author(s):

Alexandre Boumezoued

Keyword(s):

Shot Noise ◽

Noise Intensity ◽

Counting Processes ◽

Hawkes Process ◽

Process Definition ◽

Hawkes Processes ◽

Fertility Function ◽

Age Pyramid ◽

Intensity Process ◽

New Distribution

AbstractIn this paper we focus on a class of linear Hawkes processes with general immigrants. These are counting processes with shot-noise intensity, including self-excited and externally excited patterns. For such processes, we introduce the concept of the age pyramid which evolves according to immigration and births. The virtue of this approach that combines an intensity process definition and a branching representation is that the population age pyramid keeps track of all past events. This is used to compute new distribution properties for a class of Hawkes processes with general immigrants which generalize the popular exponential fertility function. The pathwise construction of the Hawkes process and its underlying population is also given.

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Reduction of shot-noise in quantum conductors

Journal de Physique IV (Proceedings) ◽

10.1051/jp4:1999203 ◽

1999 ◽

Vol 09 (PR2) ◽

pp. Pr2-23

Author(s):

L. Saminadayar ◽

A. Kumar ◽

D. C. Glattli ◽

Y. Jin ◽

B. Etienne

Keyword(s):

Shot Noise

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A Note on Shot-Noise and Reliability Modeling,

10.21236/ada151336 ◽

1984 ◽

Author(s):

A. J. Lemoine ◽

M. L. Wenocur

Keyword(s):

Shot Noise ◽

Reliability Modeling

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On the Intensity of Crossings by a Shot Noise Process.

10.21236/ada177077 ◽

1986 ◽

Author(s):

Tailen Hsing

Keyword(s):

Shot Noise ◽

Noise Process ◽

Shot Noise Process

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Suppression of Laser Shot Noise Using Laser-Cooled OptoMechanical Systems

10.21236/ada546917 ◽

2010 ◽

Author(s):

Jack G. Harris

Keyword(s):

Shot Noise ◽

Laser Shot ◽

Optomechanical Systems

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Collection and counting efficiency

10.1093/oso/9780199565092.003.0010 ◽

2017 ◽

Author(s):

A. G. Wright

Keyword(s):

Quantum Efficiency ◽

Standard Method ◽

Shot Noise ◽

Count Rate ◽

Detection Efficiency ◽

Collection Efficiency ◽

Counting Efficiency ◽

Single Electron ◽

Anode Current ◽

Secondary Electrons

Standards laboratories can provide a photocathode calibration for quantum efficiency, as a function of wavelength, but their measurements are performed with the photomultiplier operating as a photodiode. Each photoelectron released makes a contribution to the photocathode current but, if it is lost or fails to create secondary electrons at d1, it makes no contribution to anode current. This is the basis of collection efficiency, F. The anode detection efficiency, ε‎, allied to F, refers to the counting efficiency of output pulses. The standard method for determining F involves photocurrent, anode current, count rate, and the use of highly attenuating filters; F may also be measured using methods based on single-electron responses (SERs), shot noise, or the SER at the first dynode.

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