On the Optimal Dividend Problem for a Spectrally Positive Lévy Process

Abstract

In this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Lévy process before dividends are deducted. This model includes the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to an admissible strategy whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that the optimal dividend strategy is formed by a threshold strategy.

Highly computationally efficient state filter based on the delta operator

“…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.…”

“…The simulation results show that the direct state estimation algorithm can generate accurate estimates. 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. [56][57][58][59][60][61][62][63][64][65][66]…”

Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems

“…the forgetting factor BSO-HMISG algorithm (BSO-FF-HMISG) algorithm is formulated to improve the convergence speed and the parameter estimation accuracy of the BSO-HMISG algorithm. The proposed state and parameter estimation algorithms for bilinear systems can combine other estimation algorithms 45,46 and the mathematical tools [47][48][49][50][51] and strategies [52][53][54][55][56] to explore new identification methods of other linear, bilinear, and nonlinear systems with colored noises [57][58][59][60][61] and can be applied to other fields such as information processing [62][63][64][65][66] and communication. [67][68][69][70][71] Remark 6.…”

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

“…The parameter estimatêk given by the EGI algorithm depends only on the iterative counter k, not the sampling time t, and the iterative step-size k is the same. The proposed combined iterative parameter and state estimation algorithm for a class of nonlinear stochastic systems with moving average noise can combine some mathematical tools [43][44][45][46][47][48][49][50] and strategies [51][52][53][54][55] to explore new identification methods of linear and nonlinear stochastic systems and can be applied to other fields such as information processing and communication. 56 The parameter vector to be identified is In simulation, the input {u(t)} is taken as an independent persistent excitation signal sequence with zero mean and unit variance, and {v(t)} as a white noise sequence with zero mean and variance 2 = 0.10 2 , w(t) = 0.20v(t − 1) + v(t).…”