Calculation of the probability of ruin of an insurance company with consideration of reinsurance

2000 ◽  
Vol 43 (4) ◽  
pp. 251-257
Author(s):  
E. V. Glukhova ◽  
E. V. Kapustin
Keyword(s):  
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 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.

Optimal reinsurance

1970 ◽  
Vol 7 (01) ◽  
pp. 134-156 ◽  
Author(s):  
P. W. A. Dayananda
Keyword(s):  
Fundamental Principle ◽  
Expected Value ◽  
Risk Theory ◽  
Critical Study ◽  
Insurance Company ◽  
Subsequent Work ◽  
Probability Of Ruin ◽  
Optimal Reinsurance

The fundamental principle underlying insurance is that the expected value of claims is equal to the premium. This was established by Bernoulli [4] in 1738. Subsequent work on the development of ‘risk theory’ led to research concerning the probability of ‘ruin’ of an insurance company. A critical study of these investigations was made by Borch [3] in a recent paper.

scholarly journals A note on the ruin problem for a class of stochastic processes with interchangeable increments

1972 ◽  
Vol 7 (1) ◽  
pp. 81-89 ◽  
Author(s):  
Jan Grandell ◽  
Lars Peiram
Keyword(s):  
Stochastic Processes ◽  
Ruin Probabilities ◽  
Insurance Company ◽  
Probability Of Ruin ◽  
Poisson Models ◽  
Ruin Problem

SummaryModels for the risk business of an insurance company are often constructed by weighting pure Poisson models. In this paper it is verified that it is possible to calculate the probability of ruin in such weighted models by weighting ruin probabilities of pure Poisson models.

scholarly journals The rescue of an insurance company after ruin

1969 ◽  
Vol 5 (2) ◽  
pp. 280-292 ◽  
Author(s):  
Karl Borch
Keyword(s):  
Acceptable Level ◽  
Insurance Companies ◽  
Insurance Company ◽  
Recent Discussion ◽  
Probability Of Ruin ◽  
The Cost

1.1. In the different versions of the “Theory of Risk” it is almost universally assumed that ruin or bankruptcy marks the end of the game. The earlier versions of the theory tried to estimate the probability of this event, and studied the steps which an insurance company could take to bring probability of ruin down to an acceptable level. The more modern versions of the theory of risk tend to formulate the problem in economic terms, and study the cost of postponing or avoiding ruin.In a recent discussion of a paper [4] surveying the development of the theory of risk, Professor Bather suggested that ruin may not necessarily be the end. If an otherwise sound insurance company gets into difficulties, so that ruin looms large, it is very likely that steps will be taken to rescue the company, for instance by refinancing, or in more extreme cases, by a merger.1.2. To practical insurance men the simple suggestion of Professor Bather may seem next to trivial. Insurance companies get into difficulties fairly regularly, and rescue operations are considered in the insurance world, if not daily, at least annualy. The suggestion has, however, far-reaching implications for the theory of risk, and these do not seem to have been fully realised. If ruin does not mean the end of the game, but only the necessity of raising additional money, the current theories of risk may have to be radically revised. In this paper we shall discuss some of these implications.

Optimal reinsurance

1970 ◽  
Vol 7 (1) ◽  
pp. 134-156 ◽  
Author(s):  
P. W. A. Dayananda
Keyword(s):  
Fundamental Principle ◽  
Expected Value ◽  
Risk Theory ◽  
Critical Study ◽  
Insurance Company ◽  
Subsequent Work ◽  
Probability Of Ruin ◽  
Optimal Reinsurance

The fundamental principle underlying insurance is that the expected value of claims is equal to the premium. This was established by Bernoulli [4] in 1738. Subsequent work on the development of ‘risk theory’ led to research concerning the probability of ‘ruin’ of an insurance company. A critical study of these investigations was made by Borch [3] in a recent paper.

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