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 Erlangian Approximations for Finite-Horizon Ruin Probabilities

2002 ◽  
Vol 32 (2) ◽  
pp. 267-281 ◽  
Author(s):  
Soren Asmussen ◽  
Florin Avram ◽  
Miguel Usabel
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Fluid Model ◽  
Ruin Probabilities ◽  
Approximation Procedure ◽  
Exponential Form ◽  
Probability Of Ruin ◽  
Phase Type ◽  
The Matrix ◽  
The Mean

AbstractFor the Cramér-Lundberg risk model with phase-type claims, it is shown that the probability of ruin before an independent phase-type time H coincides with the ruin probability in a certain Markovian fluid model and therefore has an matrix-exponential form. When H is exponential, this yields in particular a probabilistic interpretation of a recent result of Avram & Usabel. When H is Erlang, the matrix algebra takes a simple recursive form, and fixing the mean of H at T and letting the number of stages go to infinity yields a quick approximation procedure for the probability of ruin before time T. Numerical examples are given, including a combination with extrapolation.

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.

scholarly journals On Simple Ruin Expressions in Dependent Sparre Andersen Risk Models

2014 ◽  
Vol 51 (1) ◽  
pp. 293-296 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Onno J. Boxma ◽  
Jevgenijs Ivanovs
Keyword(s):  
Explicit Formula ◽  
Exponential Type ◽  
Ruin Probability ◽  
Risk Model ◽  
General Context ◽  
Risk Models ◽  
Probability Of Ruin ◽  
Simple Alternative

In this note we provide a simple alternative probabilistic derivation of an explicit formula of Kwan and Yang (2007) for the probability of ruin in a risk model with a certain dependence between general claim interoccurrence times and subsequent claim sizes of conditionally exponential type. The approach puts the type of formula in a general context, illustrating the potential for similar simple ruin probability expressions in more general risk models with dependence.

scholarly journals MARTINGALE METHOD FOR RUIN PROBABILITY IN AN AUTOREGRESSIVE MODEL WITH CONSTANT INTEREST RATE

2003 ◽  
Vol 17 (2) ◽  
pp. 183-198 ◽  
Author(s):  
Hailiang Yang ◽  
Lihong Zhang
Keyword(s):  
Interest Rate ◽  
Autoregressive Model ◽  
Ruin Probability ◽  
Risk Model ◽  
Martingale Method ◽  
Insurance Risk ◽  
Infinite Time ◽  
Probability Of Ruin ◽  
Constant Interest Rate ◽  
Constant Interest

In this article, we consider a discrete-time insurance risk model. An autoregressive model is used to model both the claim process and the premium process. The probability of ruin is examined in a model with a constant interest rate. Both exponential and nonexponential upper bounds are obtained for the ruin probability of an infinite time horizon.

scholarly journals The probability of ruin in a reinsurance risk model with m-dependence assumptions

2021 ◽  
Author(s):  
HOANG NGUYEN HUY ◽  
NGUYEN CHUNG
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Risk Model ◽  
Random Variables ◽  
Upper Bounds ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Numerical Example ◽  
Surplus Process ◽  
Inductive Methods

In this article, we investigate a discrete-time risk model. The risk model includes the quota- (α,β) reinsurance contract effect on the surplus process. The premium process and claim process are assumed to be m-dependent sequences of i.i.d. non-negative random variables. Using Martingale and inductive methods, we obtain upper bounds for ultimate ruin probability of an insurance company. Finally, we present a numerical example to show the efficiency of the methods.

scholarly journals On a discrete-time risk model with claim correlated premiums

2015 ◽  
Vol 9 (2) ◽  
pp. 322-342 ◽  
Author(s):  
Xueyuan Wu ◽  
Mi Chen ◽  
Junyi Guo ◽  
Can Jin
Keyword(s):  
Discrete Time ◽  
Risk Model ◽  
Insurance Industry ◽  
Joint Probability ◽  
Ruin Probabilities ◽  
Deficit At Ruin ◽  
Probability Of Ruin ◽  
Numerical Examples ◽  
Car Insurance ◽  
The Impact

AbstractThis paper proposes a discrete-time risk model that has a certain type of correlation between premiums and claim amounts. It is motivated by the well-known bonus-malus system (also known as the no claims discount) in the car insurance industry. Such a system penalises policyholders at fault in accidents by surcharges, and rewards claim-free years by discounts. For simplicity, only up to three levels of premium are considered in this paper and recursive formulae are derived to calculate the ultimate ruin probabilities. Explicit expressions of ruin probabilities are obtained in a simplified case. The impact of the proposed correlation between premiums and claims on ruin probabilities is examined through numerical examples. In the end, the joint probability of ruin and deficit at ruin is also considered.

scholarly journals ASYMPTOTICS FOR A DISCRETE-TIME RISK MODEL WITH THE EMPHASIS ON FINANCIAL RISK

2014 ◽  
Vol 28 (4) ◽  
pp. 573-588 ◽  
Author(s):  
Enkelejd Hashorva ◽  
Jinzhu Li
Keyword(s):  
Discrete Time ◽  
Ruin Probability ◽  
Financial Risk ◽  
Risk Model ◽  
Tail Probability ◽  
Asymptotic Formulas ◽  
Insurance Risk ◽  
Moment Conditions ◽  
The Impact ◽  
Precise Asymptotic

This paper focuses on a discrete-time risk model in which both insurance risk and financial risk are taken into account. We study the asymptotic behavior of the ruin probability and the tail probability of the aggregate risk amount. Precise asymptotic formulas are derived under weak moment conditions of involved risks. The main novelty of our results lies in the quantification of the impact of the financial risk.

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.

The Evolving Future of Agent-Based Electronic Commerce

2011 ◽  
pp. 337-350 ◽  
Author(s):  
T. Deshani Rodrigo ◽  
Peter A. Stanski
Keyword(s):  
Electronic Commerce ◽  
Business Model ◽  
Intelligent Systems ◽  
Integrated Systems ◽  
Mobile Code ◽  
Web Based ◽  
Agent Based ◽  
On Line ◽  
The Impact ◽  
New Millennium

E-commerce technologies are continually evolving, bringing about innovative developments and resultant benefits. Herein one such visionary path for existing on-line systems to adopt is presented. An emerging set of models is discussed which combines intelligent systems, mobile code applications (MCAs) and Web-based systems. Such technologies are presented to illustrate the impact upon the numerous new value-adds for users brought about by e-commerce vendors. These are discussed in context of current developments in related fields, to expose the full gains from the integrated systems synergy. Furthermore, we conclude with an expected business model for electronic commerce in the new millennium and beyond.

scholarly journals On Simple Ruin Expressions in Dependent Sparre Andersen Risk Models

2014 ◽  
Vol 51 (01) ◽  
pp. 293-296 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Onno J. Boxma ◽  
Jevgenijs Ivanovs
Keyword(s):  
Explicit Formula ◽  
Exponential Type ◽  
Ruin Probability ◽  
Risk Model ◽  
General Context ◽  
Risk Models ◽  
Probability Of Ruin ◽  
Simple Alternative

In this note we provide a simple alternative probabilistic derivation of an explicit formula of Kwan and Yang (2007) for the probability of ruin in a risk model with a certain dependence between general claim interoccurrence times and subsequent claim sizes of conditionally exponential type. The approach puts the type of formula in a general context, illustrating the potential for similar simple ruin probability expressions in more general risk models with dependence.

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