Ruin by dynamic contagion claims

Dassios, Angelos; Zhao, Hongbiao

doi:10.1016/j.insmatheco.2012.03.006

Cited by 41 publications

(24 citation statements)

References 16 publications

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“…For more previous financial studies on market microstructure or price dynamics based on point processes or intensity modeling, the reader should refer to Bauwens and Hautsch (2009), Embrechts et al (2011), Bacry et al (2012), Zheng et al (2014) and Choe and Lee (2014a). The Hawkes process has also been applied to modeling the credit and contagion risk, see Errais et al (2010), Aït-Sahalia et al (2010) and Dassios and Zhao (2012). This paper focuses on the tick price dynamics and volatility estimation.…”

Section: Introductionmentioning

confidence: 99%

Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data

Lee

Seo

2017

Journal of Economic Dynamics and Control

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This study examine the theoretical and empirical perspectives of the symmetric Hawkes model of the price tick structure. Combined with the maximum likelihood estimation, the model provides a proper method of volatility estimation specialized in ultra-high-frequency analysis. Empirical studies based on the model using the ultra-high-frequency data of stocks in the S&P 500 are performed. The performance of the volatility measure, intraday estimation, and the dynamics of the parameters are discussed. A new approach of diffusion analogy to the symmetric Hawkes model is proposed with the distributional properties very close to the Hawkes model. As a diffusion process, the model provides more analytical simplicity when computing the variance formula, incorporating skewness and examining the probabilistic property. An estimation of the diffusion model is performed using the simulated maximum likelihood method and shows similar patterns to the Hawkes model. integer. This paper only considers the simple counting measure, i.e., k i = 1 for all i. A point process N can be regarded as a stochastic process by letting N (t, ω) = N ((−∞, t], ω). Consider a filtered probability space (Ω, {F t }, P), −∞ < t ≤ T , where the σ-field F t is generated by N (t). The Hawkes process is an orderly stationary point process N constructed by modeling the conditional intensity, λ. The conditional intensity function is represented as an adapted process toFor an M -dimensional Hawkes process (N 1 , . . . , N M is normally a deterministic function and called kernel. The integration of the r.h.s. is the stochastic integration defined pathwise. To apply the stochastic integration theory in the later, the Hawkes and intensity processes are considered to be right continuous processes with left limits. Self and mutually excited HawkesThis subsection briefly reviews the self and mutually excited Hawkes model. Consider a two dimensional Hawkes process (N 1 , N 2 ) with exponential decay kernels in the conditional intensities with constants µ i , α ij and β ij , for 0 < t:α 12 e −β12(t−u) dN 2 (u) = µ 1 + λ 11 (0)e −β11t + λ 12 (0)e −β12t + t 0 α 11 e −β11(t−u) dN 1 (u) + t 0

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Section: Introductionmentioning

confidence: 99%

Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data

Lee

Seo

2017

Journal of Economic Dynamics and Control

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“…Hawkes processes have been applied to insurance settings to accommodate the clustering arrival of claims observed in practice, see, e.g. [8,23,26,33]. When a natural disaster such as an earthquake occurs, the claims typically will not be reported following a constant intensity as in a homogeneous Poisson process.…”

Section: Example 1: Ruin Probability In Insurance Risk Theorymentioning

confidence: 99%

Large deviations and applications for Markovian Hawkes processes with a large initial intensity

Gao¹,

Zhu²

2018

Bernoulli

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Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, insurance, neuroscience, social networks, criminology, seismology, and many other fields. In this paper, we study linear Hawkes process with an exponential kernel in the asymptotic regime where the initial intensity of the Hawkes process is large. We establish large deviations for Hawkes processes in this regime as well as the regime when both the initial intensity and the time are large. We illustrate the strength of our results by discussing the applications to insurance and queueing systems.where λ(·) : R + → R + is locally integrable, left continuous, φ(·) : R + → R + and we always assume that, where τ are the occurrences of the points before time t. In the literature, 1imsart-bj ver.

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“…We extend the importance sampling methodology of Dassios and Zhao (2012) based on a suitable change of probability measure. This has a double effect:…”

Section: Ruin Probability By Change Of Measurementioning

confidence: 99%

A risk model with renewal shot-noise Cox process

Dassios

Jang

Zhao

2015

Insurance: Mathematics and Economics

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In this paper we generalise the risk models beyond the ordinary framework of affine processes or Markov processes and study a risk process where the claim arrivals are driven by a Cox process with renewal shot-noise intensity. The upper bounds of the finite-horizon and infinite-horizon ruin probabilities are investigated and an efficient and exact Monte Carlo simulation algorithm for this new process is developed. A more efficient estimation method for the infinite-horizon ruin probability based on importance sampling via a suitable change of probability measure is also provided; illustrative numerical examples are also provided.

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Ruin by dynamic contagion claims

Cited by 41 publications

References 16 publications

Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data

Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data

Large deviations and applications for Markovian Hawkes processes with a large initial intensity

A risk model with renewal shot-noise Cox process

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