On the Probability of Ruin of a Joint-Stock Insurance Company in the Sparre Andersen Risk Model

2021 ◽  
Author(s):  
A. A. Muromskaya
Keyword(s):  
Risk Model ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Sparre Andersen Risk Model

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.

Problèmes de ruine en théorie du risque à temps discret avec horizon fini

2003 ◽  
Vol 40 (3) ◽  
pp. 527-542 ◽  
Author(s):  
Philippe Picard ◽  
Claude Lefèvre ◽  
Ibrahim Coulibaly
Keyword(s):  
Risk Model ◽  
Exact Expression ◽  
Binomial Model ◽  
Insurance Company ◽  
Appell Polynomials ◽  
Probability Of Ruin ◽  
Arithmetic Distribution ◽  
Standard Compound ◽  
Compound Binomial ◽  
Compound Binomial Model

We consider a discrete-time risk model which describes the evolution of the reserves of an insurance company at periodic dates fixed in advance. The amount of loss per unit of time corresponds to independent and identically distributed random variables with arithmetic distribution, and the process of the receipt of premiums is assumed to be deterministic, nonnegative but not uniform (instead of being constant and equal to 1 as in the standard, compound binomial model). For this model, we determine the probability of ruin (or of non-ruin), as well as the distribution of the severity of the eventual ruin, with some finite horizon. A compact and efficient exact expression is found by bringing up-to-date a generalised family of Appell polynomials. The method used is illustrated with some numerical examples.

Problèmes de ruine en théorie du risque à temps discret avec horizon fini

2003 ◽  
Vol 40 (03) ◽  
pp. 527-542 ◽  
Author(s):  
Philippe Picard ◽  
Claude Lefèvre ◽  
Ibrahim Coulibaly
Keyword(s):  
Risk Model ◽  
Exact Expression ◽  
Binomial Model ◽  
Insurance Company ◽  
Appell Polynomials ◽  
Probability Of Ruin ◽  
Arithmetic Distribution ◽  
Standard Compound ◽  
Compound Binomial ◽  
Compound Binomial Model

We consider a discrete-time risk model which describes the evolution of the reserves of an insurance company at periodic dates fixed in advance. The amount of loss per unit of time corresponds to independent and identically distributed random variables with arithmetic distribution, and the process of the receipt of premiums is assumed to be deterministic, nonnegative but not uniform (instead of being constant and equal to 1 as in the standard, compound binomial model). For this model, we determine the probability of ruin (or of non-ruin), as well as the distribution of the severity of the eventual ruin, with some finite horizon. A compact and efficient exact expression is found by bringing up-to-date a generalised family of Appell polynomials. The method used is illustrated with some numerical examples.

scholarly journals Collective Value-At-Risk (Colvar) In Life Insurance Collection

2018 ◽  
Vol 7 (3.7) ◽  
pp. 25
Author(s):  
Abdul Talib Bon ◽  
Muhammad Iqbal Al-Banna Ismail ◽  
Sukono . ◽  
Adhitya Ronnie Effendie
Keyword(s):  
At Risk ◽  
Standard Deviation ◽  
Life Insurance ◽  
Value At Risk ◽  
Risk Model ◽  
Risk Measures ◽  
Model Development ◽  
Insurance Company ◽  
Insurance Claims ◽  
Level Of Significance

Analysis of risk in life insurance claims is very important to do by the insurance company actuary. Risk in life insurance claims are generally measured using the standard deviation or variance. The problem is, that the standard deviation or variance which is used as a measure of the risk of a claim can not accommodate any claims of risk events. Therefore, in this study developed a model called risk measures Collective Modified Value-at-Risk. Model development is done for several models of the distribution of the number of claims and the distribution of the value of the claim. Collective results of model development Modified Value-at-Risk is expected to accommodate any claims of risk events, when given a certain level of significance  

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 Ruin Probabilities for Two Classes of Risk Processes

2005 ◽  
Vol 35 (1) ◽  
pp. 61-77 ◽  
Author(s):  
Shuanming Li ◽  
José Garrido
Keyword(s):  
Laplace Transform ◽  
Ruin Probability ◽  
Risk Model ◽  
Compound Poisson Process ◽  
Ruin Probabilities ◽  
Counting Processes ◽  
Arrival Times ◽  
The Laplace Transform ◽  
Sparre Andersen Risk Model ◽  
Risk Processes

We consider a risk model with two independent classes of insurance risks. We assume that the two independent claim counting processes are, respectively, Poisson and Sparre Andersen processes with generalized Erlang(2) claim inter-arrival times. The Laplace transform of the non-ruin probability is derived from a system of integro-differential equations. Explicit results can be obtained when the initial reserve is zero and the claim severity distributions of both classes belong to the Kn family of distributions. A relation between the ruin probability and the distribution of the supremum before ruin is identified. Finally, the Laplace transform of the non-ruin probability of a perturbed Sparre Andersen risk model with generalized Erlang(2) claim inter-arrival times is derived when the compound Poisson process converges weakly to a Wiener process.

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.

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