Numerical Method for a Perturbed Risk Model with Proportional Investment

Wang, Chunwei; Deng, Naidan; Shen, Si-Lian

doi:10.3390/math11010043

Cited by 4 publications

(1 citation statement)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is often used in numerical calculus and numerical integration, especially in interpolation and approximation problems. In conclusion, the sinc method is a very useful tool and is widely used in numerical computation [21].…”

Section: Approximate Solution Of ϕ(U)mentioning

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Approximate Solution Of ϕ(U)mentioning

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

Self Cite

View full text Add to dashboard Cite

show abstract

Numerical Method for a Risk Model with Two-Sided Jumps and Proportional Investment

Wang

Deng

et al. 2023

Mathematics

View full text Add to dashboard Cite

In this paper, we consider a risk model with two-sided jumps and proportional investment. The upward jumps and downward jumps represent gains and claims, respectively. Suppose the company invests all of its surplus in a certain proportion in two types of investments, one is risk-free (such as bank accounts) and the other is risky (such as stocks). Our aim is to find the optimal admissible strategy (including the optimal dividend rate and the optimal ratio of investment in risky assets), to maximize the dividend value function, and discuss the effects of a number of parameters on dividend payments. Firstly, the HJB equation of the dividend value function is obtained by the stochastic analysis theory and the dynamic programming method, and the optimal admissible strategy is obtained. Since the integro-differential equation satisfied by the dividend value function is difficult to solve, we turn to the sinc numerical method to approximate solve it. Then, the error between the exact solution (ES) and the sinc approximate solution (SA) is analyzed. Finally, the relative error of a special numerical solution and an ES is given, and some examples of sensitivity analysis are discussed. This study provides a theoretical basis for insurance companies to prevent risks better.

show abstract

Two-sided jumps risk model with proportional investment and random observation periods

Wang¹,

Xu²,

Deng³

et al. 2023

MATH

View full text Add to dashboard Cite

<abstract><p>In this paper, we consider a two-sided jumps risk model with proportional investments and random observation periods. The downward jumps represent the claim while the upward jumps represent the random returns. Suppose an insurance company invests all of their surplus in risk-free and risky investments in proportion. In real life, corporate boards regularly review their accounts rather than continuously monitoring them. Therefore, we assume that insurers regularly observe surplus levels to determine whether they will ruin and that the random observation periods are exponentially distributed. Our goal is to study the Gerber-Shiu function (i.e., the expected discounted penalty function) of the two-sided jumps risk model under random observation. First, we derive the integral differential equations (IDEs) satisfied by the Gerber-Shiu function. Due to the difficulty in obtaining explicit solutions for the IDEs, we utilize the sinc approximation method to obtain the approximate solution. Second, we analyze the error between the approximate and explicit solutions and find the upper bound of the error. Finally, we discuss examples of sensitivity analysis.</p></abstract>

show abstract

Numerical Method for a Perturbed Risk Model with Proportional Investment

Cited by 4 publications

References 38 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

Numerical Method for a Risk Model with Two-Sided Jumps and Proportional Investment

Two-sided jumps risk model with proportional investment and random observation periods

Contact Info

Product

Resources

About