scholarly journals Estimation of Reinsurance Risk Value Using the Excess of Loss Method

Author(s):  
Jumadil Saputra ◽  
Tika Fauzia ◽  
Sukono Sukono ◽  
Riaman Riaman

As with any other business that has a risk of any incident in the future, the insurance business also needs protection against the risks that may arise in the company so that the company does not lose. Therefore, the need for anticipation in organizing any claims submitted by the insurance company to Reinsurance Company so that insurance company may assign any or all of the risks to reinsurance companies. In the method of reinsurance excess-of-loss there is a certain retention limits that allow reinsurance companies bear no claims incurred on insurance companies. The results of this study showed the average occurrence of claims and the risks that may be encountered by Reinsurance Company during the period of insurance. The magnitude of the risk assumed by the reinsurer relies on the model claims aggregation formed from individual claim size distribution models and distribution models the number of claims incurred in the period of insurance. Besides the magnitude of risk was also determined from the retention limit of insurance and reinsurance method used.

2006 ◽  
Vol 43 (4) ◽  
pp. 916-926 ◽  
Author(s):  
Ayalvadi Ganesh ◽  
Giovanni Luca Torrisi

We consider a class of risk processes with delayed claims, and we provide ruin probability estimates under heavy tail conditions on the claim size distribution.


2005 ◽  
Vol 35 (01) ◽  
pp. 211-238 ◽  
Author(s):  
Werner Hürlimann

The classical evaluation of pure premiums for excess of loss reinsurance with reinstatements requires the knowldege of the claim size distribution of the insurance risk. In the situation of incomplete information, where only a few characteristics of the aggregate claims to an excess of loss layer can be estimated, the method of stop-loss ordered bounds yields a simple analytical distribution-free approximation to pure premiums of excess of loss reinsurance with reinstatements. It is shown that the obtained approximation is enough accurate for practical purposes and improves the analytical approximations obtained using either a gamma, translated gamma, translated inverse Gaussian or a mixture of the last two distributions.


1996 ◽  
Vol 33 (01) ◽  
pp. 184-195 ◽  
Author(s):  
Xiaodong Lin

Bounds on the tail of compound distributions are considered. Using a generalization of Wald's fundamental identity, we derive upper and lower bounds for various compound distributions in terms of new worse than used (NWU) and new better than used (NBU) distributions respectively. Simple bounds are obtained when the claim size distribution is NWUC, NBUC, NWU, NBU, IMRL, DMRL, DFR and IFR. Examples on how to use these bounds are given.


1931 ◽  
Vol 13 (1) ◽  
pp. 1-66 ◽  
Author(s):  
Hugh W. Brown

SynopsisUnder Common Law an employer has always been liable to his workmen for his own personal negligence, but it was not until 1897 that there was enacted the first of a series of Workmen's Compensation Acts which introduced a remarkable change in the law, inasmuch as the workman was given a statutory right to compensation for accident without requiring him to prove any negligence whatever.The evolution of the law relating to Workmen's Compensation is traced through the successive Acts of Parliament, and the provisions of the Workmen's Compensation Act 1925, which codifies the law on the subject, are summarised so far as they relate to the liability covered by an Insurance Policy. Under the Act the employer is liable for personal injury to his workmen by accident “arising out of and in the course of” the employment or by certain scheduled industrial diseases.An Insurance Policy covers the liability at Common Law and under the Employers' Liability Act 1880 as well as under the Workmen's Compensation Acts, and in addition makes the Insurance Company responsible for the cost of defending claims. The injured workman may have to consider whether he is likely to recover a larger sum by way of damages than he would receive in compensation by arbitration proceedings under the Workmen's Compensation Acts, and he can then elect which course to take.A description is given of the Returns of Compensations made by Insurance Companies to the Home Office on behalf of the employers in certain selected industries as required by the Workmen's Compensation Act 1925.The requirements of the Assurance Companies Act 1909 relating to Employers' Liability Insurance business are stated. In the Annual Returns to the Board of Trade under this Act, an Actuarial Valuation of the Outstanding Claims that have been in existence for five years or more is called for on an annuity basis, but no regulations are laid down for estimating the Liability in respect of Outstanding Claims of shorter duration. The present method is to take each of such claims and after considering the facts—nature of injury, rate of compensation, etc.—to make the best possible estimate of the ultimate cost to the Insurance Company. Later developments of the injury, however, may cause such estimate to be wide of the amount which the Company is called upon to pay. A plea is advanced for an investigation into the liability in respect of Outstanding Claims, in the hope that it may be found possible to arrive at average factors which could be used, with a suitable grouping of the Claims, to determine the Liability under the non-fatal Outstanding Claims from the first occasion of their becoming outstanding. When there is no recognised method based on past experience of making such an estimate, judgment may be influenced by factors not solely relevant to the ascertainment of the liability.All the leading Offices transacting Employers' Liability Insurance business are members of the Accident Offices Association. This Association was formed after the passing of the Workmen's Compensation Act 1906, by which the scope of workmen's compensation was widely extended. The Association controls the rates and policy conditions of the Tariff Offices, but as the regulations are in great measure confidential, detailed information can only be given regarding what is already common knowledge.A further step was taken in Government supervision of Insurance Companies by the Agreement made in 1923 between the Home Office and the Accident Offices Association, the effect of which is to limit to 37½% the expenses and profits in respect of the combined figures of the members of the Association.The trend of probable future legislation as recommended by the Departmental Committee in the Insurance Undertakings Bill is described, and the questions of Compulsory Insurance and State Insurance are touched upon.An account is given of an Undertaking made recently by the Accident Offices Association to furnish the Government with workmen's compensation statistics in connection with a Home Office Scheme of enquiry into the Incidence and Causation of Accidents.The subject is so extensive that it has only been possible to deal with it in broad outline, but in conclusion reference is made to various aspects that could with advantage be expanded.


1985 ◽  
Vol 15 (2) ◽  
pp. 73-88 ◽  
Author(s):  
G. C. Taylor

AbstractThe paper deals with the renewal equation governing the infinite-time ruin probability. It is emphasized as intended to be no more than a pleasant ramble through a few scattered results. An interesting connection between ruin probability and a recursion formula for computation of the aggregate claims distribution is noted and discussed. The relation between danger of the claim size distribution and ruin probability is reexamined in the light of some recent results on stochastic dominance. Finally, suggestions are made as to the way in which the formula for ruin probability leads easily to conclusions about the effect on that probability of the long-tailedness of the claim size distribution. Stable distributions, in particular, are examined.


2022 ◽  
pp. 1-24
Author(s):  
Pengcheng Zhang ◽  
David Pitt ◽  
Xueyuan Wu

Abstract The fact that a large proportion of insurance policyholders make no claims during a one-year period highlights the importance of zero-inflated count models when analyzing the frequency of insurance claims. There is a vast literature focused on the univariate case of zero-inflated count models, while work in the area of multivariate models is considerably less advanced. Given that insurance companies write multiple lines of insurance business, where the claim counts on these lines of business are often correlated, there is a strong incentive to analyze multivariate claim count models. Motivated by the idea of Liu and Tian (Computational Statistics and Data Analysis, 83, 200–222; 2015), we develop a multivariate zero-inflated hurdle model to describe multivariate count data with extra zeros. This generalization offers more flexibility in modeling the behavior of individual claim counts while also incorporating a correlation structure between claim counts for different lines of insurance business. We develop an application of the expectation–maximization (EM) algorithm to enable the statistical inference necessary to estimate the parameters associated with our model. Our model is then applied to an automobile insurance portfolio from a major insurance company in Spain. We demonstrate that the model performance for the multivariate zero-inflated hurdle model is superior when compared to several alternatives.


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