A compound Poisson risk model with proportional investment

Chen, Xu; Ou, Hui

doi:10.1016/j.cam.2012.10.027

Cited by 15 publications

(14 citation statements)

References 9 publications

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“…For the second order systems of the integro-differential equations, it is hard to obtain analytic solutions (Chen and Ou, 2013). Therefore, we use the sinc method to gain the approximate solutions of equation ( 6).…”

Section: Numerical Sinc Methodsmentioning

confidence: 99%

“…Pioneered by Stenger (1933), the sinc method is currently widely applied to the numerical analysis, such as interpolation, quadrature, approximation of transforms, solution of integral, ordinary differential and partial differential equations (Lund and Bower, 1992;Stenger, 2000Stenger, , 2011Zarebnia and Abadi, 2010;Chen and Ou, 2013). Specifically, Chen and Ou (2013) use the sinc method to derive the integro-differential equations for the expected discounted dividend function on the interval (0, þ1).…”

Section: Numerical Sinc Methodsmentioning

confidence: 99%

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Expected discounted penalty function for a phase-type risk model with stochastic return on investment and random observation periods

Zhuo

Yang

Chen

2018

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Purpose The purpose of this paper is to build a phase-type risk model with stochastic return on investment and random observation periods to characterize the ruin quantities under which the insurance company may take effective investment strategies to avoid bankruptcy. Design/methodology/approach By the Markov property and Ito’s formula, this paper derives the integro-differential equations in which the interclaim times follow a phase-type distribution. Using the sinc method, this paper obtains the approximate solutions of the expected discounted penalty function. The numerical examples are given to verify the robustness of the proposed sinc method. Findings This paper discloses the relationship between the investment strategy and initial surplus level. The insurance company with a high initial surplus level prefers high risk portfolios to earn more profit. Contrarily, the insurance company would invest low risk portfolios to avoid bankruptcy. In addition, this paper shows that a short observation period would bring higher ruin probability. Originality/value The risk model is distinct in that a phase-type risk model is constructed with stochastic return on investment and random observation periods. These considerations in the risk model are in sharp contrast to the setting in which the stochastic return on investment is observed continuously. In practice, the insurance company only can periodically observe the surplus level to check the balance of the book. This setting, therefore, is difficult to adopt. This paper develops a sinc method to solve the approximate solutions of the expected discounted penalty function.

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Section: Numerical Sinc Methodsmentioning

confidence: 99%

Section: Numerical Sinc Methodsmentioning

confidence: 99%

Expected discounted penalty function for a phase-type risk model with stochastic return on investment and random observation periods

Zhuo

Yang

Chen

2018

Self Cite

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“…The Sinc-collocation methods are referred to Stenger [9] and have been widely used in obtaining approximate solutions of a wide class of differential and integral equations, e.g. Mohsen and EI-Gamel [10], Rashidinia and Zarebnia [11] and Chen and Ou [12].…”

Section: Integro-differential Equation and Numerical Solutionmentioning

confidence: 99%

Numerical Method for the Perturbed Risk Model with Randomized Observation and Two-sided Jumps

Dong

2018

ARJOM

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In this paper, we considered the perturbed risk model with two-sided jumps, where ruin can only occur at some Poisson times. A generalized Gerber-Shiu-type function is discussed involving the number of observations, the ruin time and the deficit at ruin. Integro-differential equations with certain boundary conditions are derived. As it is difficult to get closed-form solutions, a numerical sinc method is proposed.

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“…Similarly, using the above method, we get (21). Conditions (22) and (23) are obvious. By (14) and (15) and by the weak convergence method used in [17], it is easy to check that the boundary conditions (24) and (25) hold.…”

Section: Now We Consider the Case Ofmentioning

confidence: 99%

“…The sinc method is a highly efficient numerical method developed by Stenger, the pioneer of this field, people in his school, and others [18][19][20][21][22]. It is widely used in various fields of numerical analysis such as interpolation, quadrature, approximation of transforms, and solution of integral, ordinary differential, and partial differential equations.…”

Section: Appendixmentioning

confidence: 99%

The Perturbed Dual Risk Model with Constant Interest and a Threshold Dividend Strategy

Zeng

2013

Abstract and Applied Analysis

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We consider the perturbed dual risk model with constant interest and a threshold dividend strategy. Firstly, we investigate the moment-generation function of the present value of total dividends until ruin. Integrodifferential equations with certain boundary conditions are derived for the present value of total dividends. Furthermore, using techniques of sinc numerical methods, we obtain the approximation results to the expected present value of total dividends. Finally, numerical examples are presented to show the impact of interest on the expected present value of total dividends and the absolute ruin probability.

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A compound Poisson risk model with proportional investment

Cited by 15 publications

References 9 publications

Expected discounted penalty function for a phase-type risk model with stochastic return on investment and random observation periods

Expected discounted penalty function for a phase-type risk model with stochastic return on investment and random observation periods

Numerical Method for the Perturbed Risk Model with Randomized Observation and Two-sided Jumps

The Perturbed Dual Risk Model with Constant Interest and a Threshold Dividend Strategy

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