Gerber-Shiu Function for a Class of Markov-Modulated Lévy Risk Processes with Two-Sided Jumps

Martín-González, Ehyter M.; Murillo-Salas, Antonio; Pantí, Henry

doi:10.1007/s11009-022-09954-1

Cited by 8 publications

(3 citation statements)

References 21 publications

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“…Lin and Pavlova [6] adapted this function to the classical model. In the past ten years, the Gerber-Shiu function played an important role in the risk management of insurance companies, which has attracted wide attention from scholars [7]. Yu et al [8] and Wang et al [9] discussed the ruin problem under different models with the help of this function.…”

Section: Introductionmentioning

confidence: 99%

Based on Symmetric Jump Risk Market: Study on the Ruin Problem of a Risk Model with Liquid Reserves and Proportional Investment

Wang,

et al. 2024

Symmetry

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In order to deal with complex risk scenarios involving claims, uncertainty, and investments, we consider the ruin problems in a compound Poisson risk model with liquid reserves and proportional investments and study the expected discounted penalty function under threshold dividend strategies. Firstly, the integral differential equation of the expected discounted penalty function is derived. Secondly, since the closed-form solution of the equation cannot be obtained, a sinc method is used to obtain the numerical approximation solution of the equation. Finally, the feasibility and superiority of the sinc method are illustrated by error analysis. In addition, based on a symmetric jump risk market, we discuss the influence of some parameters on the ruin probability with some examples. This study can help actuaries develop more robust risk management strategies and ensure the long-term stability and profitability of insurance companies. It provides a theoretical basis for actuaries to carry out risk management.

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Section: Introductionmentioning

confidence: 99%

Based on Symmetric Jump Risk Market: Study on the Ruin Problem of a Risk Model with Liquid Reserves and Proportional Investment

Wang,

et al. 2024

Symmetry

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“…Te expected discounted penalty function provides a unifed framework for the evaluation of various risk quantities. For a systematic study of the Gerber-Shiu theory, one can refer to references [1][2][3][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

“…Although the expected discounted penalty function was proposed more than two decades ago and continues to play an important role in actuarial science research, there are still many unsolved problems such as the two here for generalizing the discount rate in this function from a constant to a random variable for the nonclassical risk model and looking for an efective numerical scheme for this function with no explicit solution (see [3,[5][6][7][8][9][10][11][12]).…”

Section: Introductionmentioning

confidence: 99%

On the Expected Discounted Penalty Function Using Physics-Informed Neural Network

Wang,

Wang

2023

Journal of Mathematics

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We study the expected discounted penalty at ruin under a stochastic discount rate for the compound Poisson risk model with a threshold dividend strategy. The discount rate is modeled by a Poisson process and a standard Brownian motion. By applying the differentiation method and total expectation formula, we obtain an integrodifferential equation for the expected discounted penalty function. From this integrodifferential equation, a renewal equation and an asymptotic formula satisfied by the expected discounted penalty function are derived. In order to solve the integrodifferential equation, we use a physics-informed neural network (PINN) for the first time in risk theory and obtain the numerical solutions of the expected discounted penalty function in some special cases of the penalty at ruin.

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The Gerber-Shiu discounted penalty function: A review from practical perspectives

Kawai

Shimizu

et al. 2023

Insurance: Mathematics and Economics

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Gerber-Shiu Function for a Class of Markov-Modulated Lévy Risk Processes with Two-Sided Jumps

Cited by 8 publications

References 21 publications

Based on Symmetric Jump Risk Market: Study on the Ruin Problem of a Risk Model with Liquid Reserves and Proportional Investment

Based on Symmetric Jump Risk Market: Study on the Ruin Problem of a Risk Model with Liquid Reserves and Proportional Investment

On the Expected Discounted Penalty Function Using Physics-Informed Neural Network

The Gerber-Shiu discounted penalty function: A review from practical perspectives

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