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

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Fanzi Zeng ◽  
Jisheng Xu
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Present Value ◽  
Numerical Examples ◽  
Threshold Dividend Strategy ◽  
Absolute Ruin ◽  
Dual Risk Model ◽  
The Moment ◽  
The Impact ◽  
Constant Interest

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.

RECURSIVE CALCULATION OF RUIN PROBABILITIES AT OR BEFORE CLAIM INSTANTS FOR NON-IDENTICALLY DISTRIBUTED CLAIMS

2014 ◽  
Vol 45 (2) ◽  
pp. 421-443 ◽  
Author(s):  
Anisoara Maria Raducan ◽  
Raluca Vernic ◽  
Gheorghita Zbaganu
Keyword(s):  
Continuous Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Recursive Algorithm ◽  
Risk Process ◽  
Ruin Probabilities ◽  
Numerical Examples ◽  
Claim Number ◽  
Recursive Calculation ◽  
The Impact

AbstractIn this paper, we present recursive formulae for the ruin probability at or before a certain claim arrival instant for some particular continuous time risk model. The claim number process underlying this risk model is a renewal process with either Erlang or a mixture of exponentials inter-claim times (ICTs). The claim sizes (CSs) are independent and distributed in Erlang's family, i.e., they can have different parameters, which yields a non-homogeneous risk process. We present the corresponding recursive algorithm used to evaluate the above mentioned ruin probability and we illustrate it on several numerical examples in which we vary the model's parameters to assess the impact of the non-homogeneity on the resulting ruin probability.

scholarly journals Estimating Ruin Probability in an Insurance Risk Model with Stochastic Premium Income Based on the CFS Method

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 982
Author(s):  
Yujuan Huang ◽  
Jing Li ◽  
Hengyu Liu ◽  
Wenguang Yu
Keyword(s):  
Fourier Series ◽  
Ruin Probability ◽  
Risk Model ◽  
Expansion Method ◽  
Nonparametric Estimator ◽  
Insurance Risk ◽  
Numerical Examples ◽  
Complex Fourier Series ◽  
Premium Income ◽  
Insurance Risk Model

This paper considers the estimation of ruin probability in an insurance risk model with stochastic premium income. We first show that the ruin probability can be approximated by the complex Fourier series (CFS) expansion method. Then, we construct a nonparametric estimator of the ruin probability and analyze its convergence. Numerical examples are also provided to show the efficiency of our method when the sample size is finite.

scholarly journals Gerber–Shiu Function in a Class of Delayed and Perturbed Risk Model with Dependence

Risks ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 30 ◽  
Author(s):  
Franck Adékambi ◽  
Essodina Takouda
Keyword(s):  
Time Delay ◽  
Diffusion Process ◽  
Ruin Probability ◽  
Equilibrium Distribution ◽  
Risk Model ◽  
Numerical Examples ◽  
Renewal Equations ◽  
Generalized Mixed Equilibrium ◽  
Defective Renewal Equations ◽  
Occurrence Times

This paper considers the risk model perturbed by a diffusion process with a time delay in the arrival of the first two claims and takes into account dependence between claim amounts and the claim inter-occurrence times. Assuming that the time arrival of the first claim follows a generalized mixed equilibrium distribution, we derive the integro-differential Equations of the Gerber–Shiu function and its defective renewal equations. For the situation where claim amounts follow exponential distribution, we provide an explicit expression of the Gerber–Shiu function. Numerical examples are provided to illustrate the ruin probability.

scholarly journals Discrete Time Ruin Probability for Takaful (Islamic Insurance) with Investment and Qard-Hasan (Benevolent Loan) Activities

2020 ◽  
Vol 13 (9) ◽  
pp. 211 ◽  
Author(s):  
Dila Puspita ◽  
Adam Kolkiewicz ◽  
Ken Seng Tan
Keyword(s):  
Business Model ◽  
Ruin Probability ◽  
Risk Model ◽  
Computational Procedure ◽  
Profit Sharing ◽  
Probability Of Ruin ◽  
Agent Based ◽  
Key Variables ◽  
Islamic Insurance ◽  
The Impact

The main objectives of this paper are to construct a new risk model for modelling the Hybrid-Takaful (Islamic Insurance) and to develop a computational procedure for calculating the associated ruin probability. Ruin probability is an important study in actuarial science to measure the level of solvency adequacy of an insurance product. The Hybrid-Takaful business model applies a Wakalah (agent based) contract for underwriting activities and Mudharabah (profit sharing) contract for investment activities. We consider the existence of qard-hasan facility provided by the operator (shareholder) as a benevolent loan for the participants’ fund in case of a deficit. This facility is a no-interest loan that will be repaid if the business generates profit in the future. For better investment management, we propose a separate investment account of the participants’ fund. We implement several numerical examples to analyze the impact of some key variables on the Takaful business model. We also find that our proposed Takaful model has a better performance than the conventional counterpart in terms of the probability of ruin.

scholarly journals Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments

Risks ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 110 ◽  
Author(s):  
Sooie-Hoe Loke ◽  
Enrique Thomann
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Ruin Probability ◽  
Risk Model ◽  
Constant Force ◽  
Time Of Ruin ◽  
Dual Risk Model ◽  
The Laplace Transform ◽  
Force Of Interest ◽  
The Time Of Ruin

In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the ruin probability can be well approximated for any gain distributions. Examples involving exponential, uniform, Pareto and discrete gains are considered. Finally, the same numerical method is applied to the Laplace transform of the time of ruin.

scholarly journals Estimates for the Absolute Ruin Probability in the Compound Poisson Risk Model with Credit and Debit Interest

2008 ◽  
Vol 45 (03) ◽  
pp. 818-830 ◽  
Author(s):  
Jinxia Zhu ◽  
Hailiang Yang
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Compound Poisson ◽  
Compound Poisson Risk Model ◽  
Absolute Ruin ◽  
Constant Rate ◽  
Negative Constant ◽  
The Absolute ◽  
Debit Interest ◽  
Poisson Risk Model

In this paper we consider a compound Poisson risk model where the insurer earns credit interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute ruin occurs at the moment when the surplus first drops below a critical value (a negative constant). We study the asymptotic properties of the absolute ruin probability of this model. First we investigate the asymptotic behavior of the absolute ruin probability when the claim size distribution is light tailed. Then we study the case where the common distribution of claim sizes are heavy tailed.

scholarly journals Ruin Probabilities of a Discrete-time Multi-risk Model

2015 ◽  
Vol 44 (4) ◽  
pp. 367-379 ◽  
Author(s):  
Andrius Grigutis ◽  
Agneška Korvel ◽  
Jonas Šiaulys
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Arrival Time ◽  
Risk Model ◽  
Recursive Formula ◽  
Ruin Probabilities ◽  
Numerical Examples ◽  
Premium Rate ◽  
Insurance Business ◽  
Independent Series

In this work,  we investigate a  multi-risk model describing insurance business with  two or more independent series of claim amounts. Each series of claim amounts consists of independent nonnegative random variables. Claims of each series occur periodically with some fixed   inter-arrival time. Claim amounts occur until they   can be compensated by a common premium rate and the initial insurer's surplus.  In this article, wederive a recursive formula for calculation of finite-time ruin probabilities. In the case of bi-risk model, we present a procedure to calculate the ultimate ruin probability. We add several numerical examples illustrating application  of the derived formulas.DOI: http://dx.doi.org/10.5755/j01.itc.44.4.8635

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