Probability of ruin of an insurance company for the poisson model

1999 ◽  
Vol 42 (4) ◽  
pp. 394-399 ◽  
Author(s):  
K. I. Livshits
Keyword(s):  
Poisson Model ◽  
Insurance Company ◽  
Probability Of Ruin

The impact of time discretization on solvency measurement

2017 ◽  
Vol 18 (1) ◽  
pp. 2-20 ◽  
Author(s):  
Hato Schmeiser ◽  
Daliana Luca
Keyword(s):  
Discrete Time ◽  
Risk Measures ◽  
Time Discretization ◽  
Capital Requirements ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Content Type ◽  
The One ◽  
Discretization Interval ◽  
The Impact

Purpose The purpose of this paper is to study how the discretization interval affects the solvency measurement of a property-liability insurance company. Design/methodology/approach Starting with a basic solvency model, the authors study the impact of the discretization interval on risk measures. The analysis considers the sensitivity of the discrepancy between the risk measures in continuous and discrete time to various parameters, such as the asset-to-liability ratio, the characteristics of the asset and liability processes, as well as the correlation between assets and liabilities. Capital requirements for the one-year planning horizon in continuous vs discrete time are reported as well. The purpose is to report the degree to which the deviations in risk measures, due to the different discretization intervals, can be reduced by means of increasing the frequency with which the risk measures are assessed. Findings The simulation results suggest that the risk measures of an insurance company are consistently underestimated when assessed on an annual basis (as it is currently done under insurance regulation such as Solvency II). The authors complement the analysis with the capital requirements of an insurance company and conclude that more frequent discretization translates into higher capital requirements for the insurance company. Both the probability of ruin and the expected policyholder deficit (EPD) can be reduced through intermediate financial reports. Originality/value The results from our simulation analysis suggest that that the choice of discretization interval has an impact on the risk assessment of an insurance company which uses the probability of ruin and the EPD as risk measures. By assessing the risk measures once a year, both risk measures and the capital requirements are consistently underestimated. Therefore, the recommendation for risk managers is to complement the capital requirements in solvency regulation with sensitivity analyses of the risk measures presented with respect to time discretization. On the one hand, it seems to us that there is value in knowing about the substantial discrepancy between the focused time discrete ruin probability and EPD compared to the continuous version. On the other hand, and if there are no substantial transaction costs associated with more frequent monitoring of solvency figures, a frequent update would be helpful to increase the accuracy of the calculations and reduce the EPD.

scholarly journals INSURANCE RISK WITH VARIABLE NUMBER OF POLICIES

2008 ◽  
Vol 22 (2) ◽  
pp. 213-219
Author(s):  
Ivo Adan ◽  
Vidyadhar Kulkarni
Keyword(s):  
Life Insurance ◽  
Poisson Model ◽  
Variable Number ◽  
Insurance Fund ◽  
Insurance Company ◽  
Insurance Risk ◽  
Constant Rate ◽  
Remarkable Result ◽  
New Policies ◽  
The One

In this article we consider an insurance company selling life insurance policies. New policies are sold at random points in time, and each policy stays active for an exponential amount of time with rate μ, during which the policyholder pays premiums continuously at rate r. When the policy expires, the insurance company pays a claim of random size. The aim is to compute the probability of eventual ruin starting with a given number of policies and a given level of insurance fund. We establish the remarkable result that the ruin probability is identical to the one in the standard compound Poisson model where the insurance fund increases at constant rate r and claims occur according to a Poisson process with rate μ.

scholarly journals Type II Bivariate Generalized Power Series Poisson Distribution and its Applications in Risk Analysis

2016 ◽  
Author(s):  
K.K Jose ◽  
Shalitha Jacob
Keyword(s):  
Power Series ◽  
Poisson Distribution ◽  
Counting Process ◽  
Risk Model ◽  
Poisson Model ◽  
Ruin Probabilities ◽  
Type Ii ◽  
Conditional Distributions ◽  
Generalized Power Series ◽  
Probability Of Ruin

In this paper we consider type II bivariate generalized power series Poisson distribution as a compound Poisson distribution with bivariate generalized power series compounding distribution. We obtain some properties, p.m.f. and conditional distributions. In addition we also give a brief discussion about the multivariate extension of this case. Then we introduce type II bivariate generalized power series Poisson process and consider a bivariate risk model with type II bivariate generalized power series Poisson model as the counting process. For this model we derive distribution of the time to ruin and bounds for the probability of ruin. We obtain partial integro-differential equation for the ruin probabilities and express its bivariate transform through two univariate boundary transforms,where one of the initial capitals is fixed at zero.

scholarly journals Mathematical Fun with the Compound Binomial Process

1988 ◽  
Vol 18 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Hans U. Gerber
Keyword(s):  
Joint Distribution ◽  
Classical Result ◽  
Poisson Model ◽  
Risk Theory ◽  
Binomial Model ◽  
Probability Of Ruin ◽  
Starting Point ◽  
Compound Binomial ◽  
Compound Binomial Model ◽  
Binomial Process

AbstractThe compound binomial model is a discrete time analogue (or approximation) of the compound Poisson model of classical risk theory. In this paper, several results are derived for the probability of ruin as well as for the joint distribution of the surpluses immediately before and at ruin. The starting point of the probabilistic arguments are two series of random variables with a surprisingly simple expectation (Theorem 1) and a more classical result of the theory of random walks (Theorem 2) that is best proved by a martingale argument.

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 Measuring Durability of Insurance Company Based on Ruin Probability

2020 ◽  
Vol 17 ◽  
Keyword(s):  
Exponential Distribution ◽  
Discrete Time ◽  
Ruin Probability ◽  
Claim Size ◽  
Limited Time ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Initial Capital ◽  
The Given

In this paper, we present the process of the measuring durability of insurance company, in which, this study focus on the discrete-time under the limited time the company must reserve sufficient initial capital to ensure that probability of ruin does not exceed the given quantity of risk. Therefore the illustration of the minimum initial capital under the specified period for the claim size process to the exponential distribution has explained.

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.

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