Risk processes with shot noise Cox claim number process and reserve dependent premium rate

Macci, Claudio; Torrisi, Giovanni Luca

doi:10.1016/j.insmatheco.2010.10.007

Cited by 13 publications

(8 citation statements)

References 28 publications

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“…Since the beginning of the 20th century, shot-noise processes have been extensively used to model a very wide variety of natural phenomena, with numerous applications in electronics, optics, biology and many other fields in natural science, see early literature in Campbell (1909a,b), Schottky (1918), Picinbono et al (1970) and Verveen and DeFelice (1974). More recent applications extended to insurance and actuarial science in particular can be found in Klüppelberg and Mikosch (1995), Brémaud (2000), Jang (2003, 2005), Jang (2004), Jang and Krvavych (2004), Torrisi (2004), Albrecher and Asmussen (2006), Macci and Torrisi (2011), Zhu (2013) and Schmidt (2014). Mostly, they adopted the classical Poisson shot-noise process (Cox and Isham, 1980, p.88),…”

Section: Introductionmentioning

confidence: 99%

Moments of renewal shot-noise processes and their applications

Jang

Dassios

Zhao

2018

Scandinavian Actuarial Journal

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In this paper, we study the family of renewal shot-noise processes. The Feynmann-Kac formula is obtained based on the piecewise deterministic Markov process theory and the martingale methodology. We then derive the Laplace transforms of the conditional moments and asymptotic moments of the processes. In general, by inverting the Laplace transforms, the asymptotic moments and the first conditional moments can be derived explicitly, however, other conditional moments may need to be estimated numerically. As an example, we develop a very efficient and general algorithm of Monte Carlo exact simulation for estimating the second conditional moments. The results can be then easily transformed to the counterparts of discounted aggregate claims for insurance applications, and we apply the first two conditional moments for the actuarial net premium calculation. Similarly, they can also be applied to credit risk and reliability modelling. Numerical examples with four distribution choices for interarrival times are provided to illustrate how the models can be implemented.

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Section: Introductionmentioning

confidence: 99%

Moments of renewal shot-noise processes and their applications

Jang

Dassios

Zhao

2018

Scandinavian Actuarial Journal

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“…Shen, Lin, and Zhang (2009) obtained the precise large deviation results for the customer arrival based risk model which can be treated as a generalized Poisson shot noise process. Recently, Macci and Torrisi (2011) took into account the large deviation estimations for the ruin probability of the risk processes with shot noise Cox claim number process and reserve dependent premium rate. Many researchers have made great efforts of the precise large deviations for the loss process of a classical insurance risk model and have obtained a lot of inspiring results.…”

Section: Introductionmentioning

confidence: 99%

“…Previous works on insurance applications using a shot noise process or a Cox process with shot noise intensity can be found in Brémaud (2000), Dassios and Jang (2003), Jang and Krvavych (2004), Torrisi (2004), Albrecher and Asmussen (2006), Macci and Torrisi (2011), Zhu (2013) and Schmidt (2014). However, previous study on the large deviations and moderate deviations for Cox process only gives the leading order term (Gao and Yan, 2012), but not the higher order expansion which make more accurate computational tractability for an financial application.…”

Section: Introductionmentioning

confidence: 99%

Precise deviations for Cox processes with a shot noise intensity

Cheng

Seol

2018

Communications in Statistics - Theory and Methods

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We consider a Cox process with Poisson shot noise intensity which has been widely applied in insurance, finance, queue theory, statistic, and many other fields. Cox process is flexible because its intensity not only depends on the time but also can be considered as a stochastic process and so it can be considered as a two step randomization procedure. Due to the structure of such models, a number of useful and general results can easily be established. In this paper, we study the fluctuations and precise deviations for shot noise Cox process using the recent mod-φ convergence method. MSC2010: primary 60G55; secondary 60F05, 60F10.

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“…Therefore, the shot-noise process can be used as the intensity of a Cox process to measure the number of catastrophic losses. Previous works on insurance applications using a shot-noise process or a Cox process with shot-noise intensity can be found in Klüppelberg and Mikosch (1995), Brémaud (2000), Dassios and Jang (2003), Jang and Krvavych (2004), Torrisi (2004), Dassios and Jang (2005), Albrecher and Asmussen (2006), Macci and Torrisi (2011), Zhu (2013) and Schmidt (2014).…”

Section: Introductionmentioning

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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Risk processes with shot noise Cox claim number process and reserve dependent premium rate

Cited by 13 publications

References 28 publications

Moments of renewal shot-noise processes and their applications

Moments of renewal shot-noise processes and their applications

Precise deviations for Cox processes with a shot noise intensity

A risk model with renewal shot-noise Cox process

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