The perturbed Sparre Andersen model with a threshold dividend strategy

Gao, Heli; Yin, Chuancun

doi:10.1016/j.cam.2007.08.015

Cited by 42 publications

(22 citation statements)

References 28 publications

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“…The simulation results show that the proposed algorithms can generate accurate estimates. The proposed approaches in the paper can combine other mathematical tools [64][65][66][67][68][69] and statistical strategies [70][71][72][73][74][75] to study the performances of some parameter estimation algorithms and can be applied to other multivariable systems with different structures and disturbance noises and other literature [76][77][78][79][80][81][82][83][84][85][86] such as system identification [87][88][89][90][91][92].…”

Section: Discussionmentioning

confidence: 99%

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Pan

Jiang

et al. 2018

Complexity

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The identification problem of multivariable controlled autoregressive systems with measurement noise in the form of the moving average process is considered in this paper. The key is to filter the input-output data using the data filtering technique and to decompose the identification model into two subidentification models. By using the negative gradient search, an adaptive data filtering-based gradient iterative (F-GI) algorithm and an F-GI with finite measurement data are proposed for identifying the parameters of multivariable controlled autoregressive moving average systems. In the numerical example, we illustrate the effectiveness of the proposed identification methods.

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Section: Discussionmentioning

confidence: 99%

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Pan

Jiang

et al. 2018

Complexity

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“…The identification method presented in this paper can combine iteration [37,38] and the data filtering methods to study the identification problems of linear, bilinear and nonlinear systems with different structure and disturbance noise [40][41][42]. Some mathematical skills [43][44][45][46][47][48] and statistical methods [49][50][51][52][53][54][55] can be used to study the performances of parameter estimation algorithms.…”

Section: Discussionmentioning

confidence: 99%

State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle

Zhang

Ding

et al. 2018

IET Control Theory & Applications

128

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Abstract:In the revised paper, we have highlighted the changes made in Blue FONT. This paper presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilinear systems. Thus, a bilinear state observer (BSO) is designed to give the state estimates using the extremum principle. Then a BSO based recursive least squares (BSO-RLS) algorithm is developed. For comparison with the BSO-RLS algorithm, by dividing the system into three fictitious subsystems on basis of the decomposition-coordination principle, a BSO based hierarchical least squares algorithm is proposed to reduce the computation burden. Moreover, a BSO based forgetting factor recursive least squares algorithm is presented to improve the parameter tracking capability. Finally, a numerical example illustrates the effectiveness of the proposed algorithms. IntroductionParameter estimation is a significant part in system identification, and has been widely used in system analysis [1][2][3], system modeling [4][5][6][7], and system control [8,9]. Since many industrial processes are complex and inherently nonlinear, nonlinear system identification has drawn much attention throughout the world [10][11][12]. The bilinear approach for modeling these complex processes are proven to be more precise than any other traditional linear models [13]. However, the nonlinear term existing in the bilinear model brings some challenges for bilinear system identification. During the past decades, much work has been carried out on parameter estimation for bilinear systems. For example, dos Santos et al. presented a subspace identification method for bilinear systems by treating the bilinear term as a second-order white noise process [14]. Larkowski et al. addressed the identification problem of the diagonal bilinear errors-in-variables system and extended the bias compensated least squares technique to bilinear systems [15]. Li et al. applied the polynomial transformation technique to obtain the equivalent input-output representation of the bilinear system and proposed the iterative algorithm for parameter estimation [16][17][18]. The recursive least squares (RLS) approach is known as the most commonly used estimation method among numerous different parameter estimation techniques. Although the RLS method offers a fast convergence rate, there exists several problems such as the increase in the computational burden and the decline in the tracking capability [19,20]. The hierarchical identification principle is applied to decompose a bilinear system into several subsystems Nonlinear filtering techniques have attracted much attention in signal processing [26,27] and have wide applications in many areas [28][29][30][31]. The classical Kalman filter (KF) is recognized as the best linear filter for linear systems under Gaussian noises. However, it is not suitable f...

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“…[16] considered dividend payments with a threshold strategy in the compound Poisson risk model perturbed by diffusion. [4] extended the results of [16] via assuming that the interclaim times follow a generalized Erlang(n) distribution. As a more general framework, [3] considered surplus processes of which the claim number is a Markovian arrival process perturbed by diffusion with dividend barrier strategies.…”

Section: Introductionmentioning

confidence: 96%

Dividend moments for two classes of risk processes with phase-type interclaim times

Jiang¹

2015

HJMS

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In this paper, we consider the distribution of discounted dividend payments until ruin under a risk model with two independent classes of claims in which both of the two interclaim times have phasetype distributions and a constant dividend barrier. We obtain the integro-differential equations with boundary conditions for the momentgenerating function of the sum of the discounted dividend payments until ruin. Explicit expressions for arbitrary moments of the discounted dividend payments are derived if the distribution of the two classes claim amount both belong to the rational family. Finally, numerical illustrations are presented to show how the results are applied.

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The perturbed Sparre Andersen model with a threshold dividend strategy

Cited by 42 publications

References 28 publications

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Adaptive Gradient‐Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

State filtering‐based least squares parameter estimation for bilinear systems using the hierarchical identification principle

Dividend moments for two classes of risk processes with phase-type interclaim times

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