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Škodne rezervacije predstavljajo pomemben del obveznosti premoženjskih zavarovalnic, zato je njihov izračun ključnega pomena. V splošnem jih sestavljajo rezervacije za že prijavljene škode ter rezervacije za še ne prijavljene škode. Delo opisuje pragmatično metodo za izračun rezervacij za že prijavljene škode. Metoda s pomočjo informacij preteklih škod oblikuje stohastične napovedi razvojev individualnih škod. Pri tem, poleg končnih višin škod napove tudi pripadajoče razvoje likvidiranih in nastalih vrednosti. Za razliko od večine obstoječih metod pri tem uporablja informacije individualnih škod, in sicer tako informacije o likvidiranih kot tudi nastalih vrednostih. Predlagana metoda je ovrednotena na sintetičnih portfeljih. Izhodišče za primerjavo so dejanske vrednosti sintetičnih podatkov ter napovedi metode veriženja—ene najbolj znanih metod za izračun rezervacij. V primeru homogenih portfeljev so napovedi obeh omenjenih metod primerljive s pravimi vrednostmi sintetičnih podatkov. Ker pa predlagana metoda uporablja informacije individualnih škod, so njene napovedi precej boljše v primeru nehomogenih portfeljev. Loss reserves represent an important component of non-life insurance companies' liabilities, making their accurate calculation essential. Generally, loss reserves consist of two components: reserves for already reported claims and reserves for claims that are yet to be reported. The work presents a pragmatic method for calculating reserves for reported claims that utilizes a case-based reasoning paradigm. The proposed method uses historical data to generate stochastic predictions of individual claims developments, including ultimate claim amounts and corresponding developments of both paid and incurred amounts. Unlike most existing methods, the proposed method leverages individual claim information and uses paid as well as incurred data. The proposed method is evaluated using synthetic portfolios. The actual values of synthetic data and the predictions of the chain ladder method—a widely used method for loss reserving—are used as benchmarks. Results indicate that for homogeneous portfolios, both methods' predictions are similar to the actual values of synthetic data. However, because the proposed method uses individual claims information, it shows improved performance over the chain method in the case of heterogeneous portfolios.

We analyse characteristics of the three most commonly used methods for estimating loss reserves in non life insurance: the chain ladder method, the loss ratio method, and the Bornhuetter-Ferguson method. Our aim is to give a comparative analysis of the results obtained from applying these methods to a practical case, and to put emphasis on their advantages and disadvantages. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 179005: The risks of financial institutions and markets in Serbia - microeconomic and macroeconomic approach]

We examine the relation between loss reserving errors, leverage and reinsurance in the UK's property-casualty insurance industry. We find that financially weak insurers under-estimate reserves to reduce leverage, and so pre-empt costly regulatory scrutiny. However, at very high leverage, insurers over-reserve, suggesting a non-linear relation between leverage and reserving policy. We also investigate whether monitoring by reinsurers reduces reserving errors, and find that highly reinsured insurers are less likely to make loss reserve errors. However, the use of proportional reinsurance does not affect loss reserve accuracy.

Rejting i pozicioniranje osiguravača na sve konkurentnijem, veoma nerazvijenom tržištu osiguranja u Republici Srbiji, determinisani su visinom premije osiguranja i mobilnošću i brzinom isplate podnetih zahteva. Ovi markeri kredibiliteta poslovanja zavise od količine novčanih sredstava usmerene na isplate nastalih potraživanja. Tehničke rezerve, kao akumulirana sredstva iz fakturisanih premija, predstavljaju pokušaj da se u nekom vremenskom trenutku odredi finansijska implikacija celokupnog portfelja osiguranja. Procena njihovog iznosa je komplikovana, zbog inherentne neizvesnosti o trenutku, broju i veličini mogućih gubitaka osiguranika. Ove komponente etabliraju kvantifikaciju tehničkih rezervi u neživotnom osiguranju kao veoma aktuelnu i kompleksnu istraživačku oblast i predmet interesovanja kako menadžmenta tako i brojnih aktuara i naučnika. Primarni istraživački interes disertacije leži u analizi matematičko- statističkih metoda i modela obračuna pojedinih komponenti tehničkih rezervi u aktuarskoj praksi Republike Srbije, koja nije dovoljno analizirana u domaćim akademskim krugovima. Kako jaka privredna i ekonomska kriza, koja inhibira razvoj i napredak osiguranja, tangira i ostale privredne aktere, analiza interakcija premija, tehničkih rezervi i solventnosti poslovanja osiguravača praćena je istraživačkim modelom, usmerenim na komparativnu analizu finansijskih i nefinansijskih performansi osiguravajućih društava sa odgovarajućim performansama ostalih privrednih subjekata. Identifikovani uticaj neadekvatnog nivoa troškova sprovođenja osiguranja potvrđuje da kvantifikovanje iznosa tehničkih rezervi, kao i adektavtnog monitoringa nad pojedinim generatorima njihovog iznosa, predstavlja glavni katalizator koncentovanije prakse i kvalitetnijeg poslovanja domaćih osiguravajućih društava, kao sigurnih i stabilnih partnera pri suočavanju sa rizicima i neizvesnošću koje budućnost donosi. Rating and positioning of insurers in a more competitive market, but underdeveloped insurance market in the Republic of Serbia, are determined by insurance premium rate, mobility and the speed of collection based on the submitted requests. These business operations credibility markers depend on the sum of financial resources intended to settling liabilities. Technical reserves, as accumulated resources originating from invoiced premiums, represent an attempt to determine financial implications of the overall insurance portfolio at a given time. An estimate of their sums is uncertain due to inherent uncertainty regarding the moment, number and size of potential losses of the insured persons. These components establish the quantification of technical reserves in nonlife insurance as a current and complex research field, as well as the subject of interest on the part of management and numerous actuaries and scientists. Primary research interest expressed in this dissertation refers to the analysis of mathematicalstatistical methods and models of calculating individual components of technical reserves in actuary practice which is not sufficiently explored in the academia of the Republic of Serbia. Given the fact that acute economic crisis, which inhibits development and prosperity of the insurance field, affects other business players, the analysis of the interaction among premium, technical reserves and business solvency is accompanied with a research model encompassing comparative analysis of financial and non - financial performance of insurance companies with corresponding performance of other economic entities. The identified influence of inadequate expenses levels in administering insurance confirms that the evaluation of technical reserve sums, as well as the adequate monitoring over individual generators of such sums represents principal catalyst of concentrated practice and better quality of business operations of domestic insurance companies, as secure and stabile partners in facing risks and uncertainties that may arise in the future.

In this paper we give some methods to set up confidence bounds for the discounted IBNR reserve. We start with a loglinear regression model and estimate the parameters by maximum likelihood methods such as e.g. given in Doray, 1996. We want to find an answer to the following question: 'What is the amount we have to reserve at time 0 in order to be able to meet our future obligations?' The knowledge of the distribution function of the discounted IBNR reserve(S) will help us to determine the initial reserve . E.g. we could determine this reserve as , or , to assume with 95% confidence that we can meet our future obligations. The results are based on convex order techniques, such that our approximations for the distribution function of S are larger or smaller, in convex order sense, than the 'true distribution function of S'. ispartof: DTEW Research Report 0263 pages:1-30 status: published