Title: Technical reserves of non-life insurance in the internal solvency model Author: Bc. Jiří Thomayer Department: Department of Propability and Mathematical Statistics Supervisor: Mgr. Ing. Jakub Mertl Abstract: In this work we study and describe calculation of solvency capital using the standard formula contained in the Directive of the European Union (Solvency II), which should be put into practice in Europe on 1 January 2013. This calcu- lation is described in quantitative impact study 5. We describe a general approach to risk measurement and we show some particular practical measures used to risk measurement. We explain under what conditions the standard formula or its parts can be replaced by internal model. Next, we show disadvantages of using the stan- dard formula and we propose possible internal model to calculate risk premiums and risk reserves in non-life insurance. Finally we apply the proposed model for calculation risk reverses in non-life insurance in practice. Keywords: Standard formula, Risk measurement, Solvency II, Internal model;

The diploma thesis focuses on the topic of the future regulatory regime of the insurance and reinsurance market of the European Union called Solvency II. Currently the most discussed issue without a final structure is an extensive set of legislative and technical changes not only in the area of solvency treatment. Primarily, the work focuses on the standard formula calculation of capital requirements that reflect the solvency position of companies on the market. The first part deals with the theoretical description of the calculating methods of the required capital levels under current and future rules on the basis of available official documents. Further the general overview of the Solvency II is presented, a more detailed description of the valuation techniques of balance sheet items for the purposes of Solvency II, dealing with company's own funds and possible ways to optimize the asset portfolio are also included. Some theoretical descriptions of computational procedures applied on a fictitious life insurance company are presented in the second, more practical part of the diploma thesis.

This thesis introduces various approaches to natural catastrophe risk assessment in (re)insurance environment. Most emphasis and further elaboration is put on probabilistic models in comparison to the standard model as proposed by Solvency II. The outcomes of natural catastrophe modeling play an important role in the design of proper actuarial models related to catastrophe risk. More specifically it is shown that they can be entirely understood in a wider actuarial context, namely risk theory. Within the Solvency II framework, probabilistic model outcomes are translated by means of the proposed decomposition methodology putting them into a similar language of the standard formula in order to create the ability to compare different results implied by either probabilistic model or standard formula. This enables both comparison of the implied dependence structure of probabilistic model to standardized correlations assumed in Solvency II, and scenario year loss factors of Solvency II to implied damage factors of probabilistic models in defined cresta zones. The introduced decomposition methodology is illustrated by flood and windstorm model outcomes calculated on exposure data of Czech insurance companies and compared to the respective standard formula parameters and outcomes. Finally, other applications of the proposed decomposition methodology are introduced, such as measurement of diversification effect or blending of different results calculated by different models or even approaches to natural catastrophe risk assessment.

Detta examensarbetes syfte var att undersöka möjligheter till förbättring av hantering av lagernivåer för Bygg Ole Saltsjö-Boo. En kombination av aspekter från både systemteknik och industriell ekonomi har använts. I rapporten applicerades Guaranteed Service-Level modellen baserad på historisk försäljning i kombination relevanta teorier om lagerkostnad. Rapporten var begränsad till att behandla utvalda produkter med hög omsättning från två utvalda leverantörer till Bygg Ole. Efterfrågan för alla produkter i rapporten utom en är icke säsongsberoende. Särskild hänsyn har dessutom tagits till servicenivå, kapitalkostnader och variation i efterfråga. Resultatet gav att en implementering av modellen skulle ge lägre lagernivåer och därmed lägre lagerkostnader. Slutsatsen från rapporten var att modellen skulle kunna implementeras, eventuellt med höga administrativa kostnader i början. Bygg Ole har också en möjlighet att använda ett ordersystem baserat på den matematiska GSL-modellen (Guaranteed Service-Level) i kombination med prognoser över efterfrågan producerade av försäljningsavdelningen på Bygg Ole. Detta skulle potentiellt kunna öka precisionen i lagerhanteringen. Den nuvarande lagerräntan är relativt lågt bestämd och därför minskas de beräknade besparingarna från implementering av modellen. Om lagerräntan skulle vara högre skulle den ekonomiska fördelen med implementeringen vara tydligare. Rekommendationen till Bygg Ole är att tillämpa den rekommenderade GSL-modellen i kombination med ett system för prognos över efterfrågan på några utvalda produkter och sedan utvärdera resultatet. / The aim of this thesis was to examine possible improvements in the inventory management and procedure of ordering at Bygg Ole Saltsjö-Boo. A combination of aspects from both Systems Engineering and Industrial Engineering and Management has been used. In the report, a Guaranteed Service-Level model based on historical data of sales in combination with relevant theories about inventory carrying cost has been applied. The study was limited to specific chosen products with high sales from two selected suppliers of Bygg Ole. All these products in the study except one experienced low seasonal variety in demand. Furthermore special consideration was taken to service level, cost of capital and variability of demand. The result was that an implementation of the model would yield lower inventory levels and therefore lower carrying costs of inventory. The conclusion from the report was that the model could be implemented, although with possibly high administrative costs in the beginning. Bygg Ole also has a possibility of using an ordering system based on the mathematical GSL-model (Guaranteed Service-Level) in combination with forecasts of demand conducted by the sales department of Bygg Ole. This could potentially increase precision in the inventory management. The current inventory carrying charge is compounded relatively low and therefore decreases the calculated savings from implementing the model. If the carrying charge would be higher, the benefits of implementation would be more evident. The recommendation for Bygg Ole is to apply the recommended GSL-model in combination with a demand forecast planning system on a few selected products and then evaluate the result.

The purpose of this project is to validate the adequacy of the Standard formula, used to calculate the Solvency Capital Requirement (SCR), with respect to a Swedish insurance company. The sub-modules evaluated are Equity risk (type 1) and Interest rate risk. The validation uses a quantitative assessment and the concept of Value at Risk (VaR). Additionally, investment strategies for risk free assets are evaluated through a scenario based analysis. The findings support that the Equity shock of 39%, as proposed in the Standard formula, is appropriate for a diversified portfolio of global equities. Furthermore, to some extent; the Equity shock is also sufficient for a diversified global portfolio with an overweight of Swedish equities. Additionally, the findings shows that the Standard formula for Interest rate risks occasionally underestimates the true Interest rate risk. Furthermore, it’s shown that there are some advantage of selecting an investment strategy that stabilizes the Own fund of an insurance company rather than a strategy that minimizes the SCR. / Syftet med detta arbete är att utvärdera Standardformeln, som används för att beräkna solvenskapitalkravet (SCR) under Solvens II, med avseende på dess lämplighet för ett svensk försäkringsbolag. Modulerna som utvärderas är aktierisk (typ 1) och ränterisk. Utvärderingen genomförs med kvantitativa metoder och utifrån konceptet Value at Risk (VaR). Dessutom utvärderas investeringsstrategier för riskfria tillgångar genom en scenariobaserad analys. Resultaten stödjer att den av Standardformeln föreskrivna aktiechocken på -39 % är tillräcklig för en diversifierad global aktieportfölj. Dessutom är aktiechocken även tillräcklig för en diversifierad global portfölj med en viss övervikt mot svenska aktier. Vidare visar resultaten att Standardformeln under vissa omständigheter underskattar ränterisken. Slutligen visar den scenariobaserade analysen att det är fördelaktigt att välja en investeringsstrategi som stabiliserar Own fund, hellre än en strategi som minimerar SCR.