Exit problems for jump processes with applications to dividend problems

Yin, Chuancun; Shen, Ying; Wen, Yuzhen

doi:10.1016/j.cam.2012.12.004

Cited by 108 publications

(60 citation statements)

References 21 publications

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“…The following lemmas have been derived by Yin et al (2013) (see Lemmas 2.2, 2.4 and 2.5), and one can refer to that paper for the details of the proofs. …”

Section: Resultsmentioning

confidence: 99%

The time of deducting fees for variable annuities under the state-dependent fee structure

Zhou

2015

Insurance: Mathematics and Economics

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“…The following lemmas have been derived by Yin et al (2013) (see Lemmas 2.2, 2.4 and 2.5), and one can refer to that paper for the details of the proofs. …”

Section: Resultsmentioning

confidence: 99%

The time of deducting fees for variable annuities under the state-dependent fee structure

Zhou

2015

Insurance: Mathematics and Economics

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“…The methods proposed in this paper can combine some statistical methods [48][49][50][51][52][53][54][55] to study the parameter identification and state filter design for different systems with colored noise and can be applied to other fields. A state estimation algorithm based on the Kalman filtering principle is proposed for comparison.…”

Section: Discussionmentioning

confidence: 99%

Highly computationally efficient state filter based on the delta operator

Xiao

Ding

et al. 2019

Adaptive Control & Signal

160

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The Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm.

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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%

“…So the algorithm in (15)-(17) cannot be used directly to estimate the system states x(t). The method is to use the estimated parametersâ(t),b(t) andf (t) obtained by the parameter estimation algorithm in (42)- (50) to construct the estimates of the system parameter matrices and parameter vectorÂ(t),B(t) and f (t) to take place of A, B and f . Similarly, replacing x(t) in ϕ(t) withx(t) gives the estimatesφ x (t),φ xu (t) andφ(t) in (42)-(50).…”

Section: The Bso Based Hierarchical Least Squares Algorithmmentioning

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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Exit problems for jump processes with applications to dividend problems

Cited by 108 publications

References 21 publications

The time of deducting fees for variable annuities under the state-dependent fee structure

The time of deducting fees for variable annuities under the state-dependent fee structure

Highly computationally efficient state filter based on the delta operator

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

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